subject:( Gross Pitaevskii equation)

Univerzitet u Beogradu

1. Petrović, Nikola Z. Tačna talasna i solitonska rešenja generalisane nelinearne Šredingerove jednačine.

Degree: Fizički fakultet, 2015, Univerzitet u Beogradu

URL: https://fedorabg.bg.ac.rs/fedora/get/o:7042/bdef:Content/get

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Nonlinear optics-Mathematical physics / Нелинеарна оптика-Примена математичке физике

Напредак у нелинеарној оптици умногоме зависи од наше способности да нађемо нова решења разних диференцијалних једначина које… (more)

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Nonlinear optics-Mathematical physics / Нелинеарна оптика-Примена математичке физике

Напредак у нелинеарној оптици умногоме зависи од наше способности да нађемо нова решења разних диференцијалних једначина које се природно јављају у системима где светлост интерагује са нелинеарном средином. Иако су рекреирање ових система кроз експеримент и компјутерска симулација система два најчешћа и плодотворна приступа, крајњи циљ остаје да се нађу егзактна решења ових система. Циљ ове тезе је да комбинује раније технике налажења егзактних решења диференцијалних једначина и примени их на нелинеарну Шредингерову диференцијалну једначину (НШДЈ). Конкретно, настао је недавно пробој у применама одређених техника експанзије у налажењу одређених егзактних решења НШДЈ. Упркос ограничењу у комбиновању решења због нелинеарности система и чињенице да не могу општа решења да се нађу, сама чињеница да можемо идентификовати нека егзактна решења је од великог значаја за област, посебно код евалуирања какве су појаве могуће у таквим системима. Ова теза ће се фокусирати на примену технике Ф-експанзије користећи се Јакобијевим елиптичним функцијама (ЈЕФ) да би се решиле разне форме НШДЈ са нелинеарношћу трећег степена. НШДЈ са нелинеарношћу трећег степена је од фундаменталне важности за област нелинеарне оптике јер описује путовање светлости кроз материјал са Керовом нелинеарношћу. Одређеним модификацијама технике Ф-експанзије можемо наћи егзактна решења за широку класу система. Системи које ја презентујем у тези имају одређен скуп заједничких особина. Све једначине имају једну лонгитудиналну промењиву, или просторну или временску, због параксијалне апроксимације, и до три трансферзалне димензије, такође или просротне или временске понаособ. Ако су све трансферзалне вариабле просторне vii онда суму њихових других извода множим са коефицијентом дифракције β, а ако је нека од варијабли темпорална, онда говорим о коефицијенту дифракције/дисперзије. Та два коефицијента (дифракција и дисперзија) могу да се нормализују у један до на знак. У случају аномалне дисперзије коефицијенти имају исти знак, а у случају нормалне дисперзије супротан знак. Осим ова два коефицијента редукована у један, имамо такође и коефицијент χ који одређује јачину нелинеарности трећег степена, и коефицијент γ који одређује добитак (за позитивно γ) или губитак сигнала у нашем систему...

Advisors/Committee Members: Belić, Milivoj.

Subjects/Keywords: Јacobi elliptic function nonlinear Schrödinger equation Gross-Pitaevskii

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Petrović, N. Z. (2015). Tačna talasna i solitonska rešenja generalisane nelinearne Šredingerove jednačine. (Thesis). Univerzitet u Beogradu. Retrieved from https://fedorabg.bg.ac.rs/fedora/get/o:7042/bdef:Content/get

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Petrović, Nikola Z. “Tačna talasna i solitonska rešenja generalisane nelinearne Šredingerove jednačine.” 2015. Thesis, Univerzitet u Beogradu. Accessed April 14, 2021. https://fedorabg.bg.ac.rs/fedora/get/o:7042/bdef:Content/get.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Petrović, Nikola Z. “Tačna talasna i solitonska rešenja generalisane nelinearne Šredingerove jednačine.” 2015. Web. 14 Apr 2021.

Vancouver:

Petrović NZ. Tačna talasna i solitonska rešenja generalisane nelinearne Šredingerove jednačine. [Internet] [Thesis]. Univerzitet u Beogradu; 2015. [cited 2021 Apr 14]. Available from: https://fedorabg.bg.ac.rs/fedora/get/o:7042/bdef:Content/get.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Petrović NZ. Tačna talasna i solitonska rešenja generalisane nelinearne Šredingerove jednačine. [Thesis]. Univerzitet u Beogradu; 2015. Available from: https://fedorabg.bg.ac.rs/fedora/get/o:7042/bdef:Content/get

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Michigan State University

2. Chen, Anqi. On superconvergent discontinuous Galerkin methods for Schrödinger equations and sparse grid central discontinuous Galerkin method.

Degree: 2019, Michigan State University

URL: http://etd.lib.msu.edu/islandora/object/etd:48238

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Thesis Ph. D. Michigan State University. Applied Mathematics 2019.

"In this thesis, we design and analyze a discontinuous Galerkin (DG) method for one-dimensional Schrodinger equations… (more)

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Thesis Ph. D. Michigan State University. Applied Mathematics 2019.

"In this thesis, we design and analyze a discontinuous Galerkin (DG) method for one-dimensional Schrodinger equations under a general class of numerical fluxes, and another efficient DG method for high-dimensional hyperbolic equations.In the first DG method, we develop an ultra-weak discontinuous Galerkin (UWDG) method to solve the one-dimensional nonlinear Schrödinger equation. Stability conditions and error estimates are derived for the scheme with a general class of numerical fluxes. The error estimates are based on detailed analysis of the projection operator associated with each individual flux choice. Depending on the parameters, we find out that in some cases, the projection can be defined element-wise, facilitating analysis. In most cases, the projection is global, and its analysis depends on the resulting 2 x 2 block-circulant matrix structures. For a large class of parameter choices, optimal a priori L2 error estimates can be obtained. Numerical examples are provided verifying theoretical results.In addition to the stability and error analysis, we analyze the superconvergence properties of the UWDG method for one-dimensional linear Schrodinger equation with various choices of flux parameters. Depending on the flux choices and if the polynomial degree k is even or odd, we prove 2k or (2k - 1)-th order superconvergence rate for cell averages and numerical flux of the function, as well as (2k - 1) or (2k - 2)-th order for numerical flux of the derivative. In addition, we prove superconvergence of (k + 2) or (k + 3)-th order of the UWDG solution towards a special projection. At a class of special points, the function values and the first and second order derivatives of the UWDG solution are superconvergent with order k + 2, k + 1, k, respectively. The proof relies on the correction function techniques initiated in Cao, et. al. (2014), and applied to Cao, et. al. (2017) for direct DG (DDG) methods for diffusion problems. By negative norm estimates, we apply the post processing technique and show that the accuracy of our scheme can be enhanced to order 2k. Theoretical results are verified by numerical experiments.In the second DG method, we develop sparse grid central discontinuous Galerkin (CDG) scheme for linear hyperbolic systems with variable coefficients in high dimensions. The scheme combines the CDG framework with the sparse grid approach, with the aim of breaking the curse of dimensionality. A new hierarchical representation of piecewise polynomials on the dual mesh is introduced and analyzed, resulting in a sparse finite element space that can be used for non-periodic problems. Theoretical results, such as L2 stability and error estimates are obtained for scalar problems. CFL conditions are studied numerically comparing discontinuous Galerkin (DG), CDG, sparse grid DG and sparse grid CDG methods. Numerical results including scalar linear equations, acoustic and elastic waves are provided." – Pages ii-iii.

Description based on…

Advisors/Committee Members: Cheng, Yingda, Christlieb, Andrew J, Chiu, Chichia, Qian, Jianliang.

Subjects/Keywords: Galerkin methods; Schrödinger equation; Gross-Pitaevskii equations; Applied mathematics; Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Chen, A. (2019). On superconvergent discontinuous Galerkin methods for Schrödinger equations and sparse grid central discontinuous Galerkin method. (Thesis). Michigan State University. Retrieved from http://etd.lib.msu.edu/islandora/object/etd:48238

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Chen, Anqi. “On superconvergent discontinuous Galerkin methods for Schrödinger equations and sparse grid central discontinuous Galerkin method.” 2019. Thesis, Michigan State University. Accessed April 14, 2021. http://etd.lib.msu.edu/islandora/object/etd:48238.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Chen, Anqi. “On superconvergent discontinuous Galerkin methods for Schrödinger equations and sparse grid central discontinuous Galerkin method.” 2019. Web. 14 Apr 2021.

Vancouver:

Chen A. On superconvergent discontinuous Galerkin methods for Schrödinger equations and sparse grid central discontinuous Galerkin method. [Internet] [Thesis]. Michigan State University; 2019. [cited 2021 Apr 14]. Available from: http://etd.lib.msu.edu/islandora/object/etd:48238.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Chen A. On superconvergent discontinuous Galerkin methods for Schrödinger equations and sparse grid central discontinuous Galerkin method. [Thesis]. Michigan State University; 2019. Available from: http://etd.lib.msu.edu/islandora/object/etd:48238

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

3. Mohamad, Haidar. Sur l'équation de Gross-Pitaevskii uni-dimensionnelle et quelques généralisations du flot par courbure binormale : On the one-dimensional Gross-Pitaevskii equation and some generalisations of the binormal curvature flow.

Degree: Docteur es, Mathématiques Appliquées, 2014, Université Pierre et Marie Curie – Paris VI

URL: http://www.theses.fr/2014PA066176

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Ce travail est une contribution à l'étude des équations de Schrödinger non-linéaires (NLS) en dimension un d'espace. De telles équations interviennent notamment comme modèles dans… (more)

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Ce travail est une contribution à l'étude des équations de Schrödinger non-linéaires (NLS) en dimension un d'espace. De telles équations interviennent notamment comme modèles dans plusieurs domaines de la physique mathématique, tels l'optique non-linéaire, la superfluidité, la supraconductivité et la condensation de Bose-Einstein.Cette thèse contient trois thèmes connexes inclus dans les chapitres 2, 3 et 4. Dans la première partie (chapitre 2), on s'intéresse à la construction des solutions en multi-solitons de l'équation de Gross-Pitaevskii (NLS défocalisante avec non-linéarité cubique), comme une superposition approximative des ondes progressives (solitons). Cette partie contient également une description détaillée des interactions entre les solitons. Ces résultats sont obtenus en exploitant l'intégrabilité de l'équation de Gross-Pitaevskii et son système de Marchenko associé.La deuxième partie (chapitre 4) clarifie les relations entre la formulation classique et la formulation dite hydrodynamique de l'équation de Gross-Pitaevskii. Cette dernière a un sens lorsque la solution ne s'annule jamais dans le domaine spatial. La dernière partie (chapitre 3) est consacrée à l'étude du problème de Cauchy d'une famille d'équations aux dérivées partielles quasi-linéaires qui généralise l'équation du flot par courbure binormal d'une courbe dans l'espace euclidien de dimension trois. Cette dernière est liée formellement à NLS par la transformation de Hasimoto. Dans notre généralisation, la vitesse d'un point de la courbe est toujours dirigée dans la direction du vecteur binormal, mais son amplitude peut dépendre de l'abscisse curviligne ainsi de la position dans l'espace. Notre approche pour prouver l'existence est le suivant: schéma semi-discret (discret en espace et continu en temps), obtention de bornes sur les problèmes discrets et argument par compacité. Un théorème de comparaison entraîne l'unicité.

This work is a contribution to the study of nonlinear Schrödinger equations (NLS) in the one-dimensional space. Such equations arise in many physical fields, including nonlinear optics and Bose-Einstein condensation. The thesis contains three connected themes included in chapters 2, 3 and 4. The first part (chapter 2) constructs multi-soliton solutions of the Gross-Pitaevskii (or defocussing NLS) equation, as an approximate superposition of traveling waves (solitons). This part contains also a detailed description of the interactions between solitons. These results are obtained by exploiting the integrability of the the Gross-Pitaevskii equation and its associated Marchenko system. The second part (chapter 4) clarifies the relations between the classical formulation and the so-called hydrodynamical formulation that only has a meaning when the solution does not vanish anywhere in the spatial domain The last part (chapter 3) of this thesis concerns existence and uniqueness results for a family of quasi-linear partial differential equations that generalize the equation of the binormal curvature flow for a curve in the…

Advisors/Committee Members: Smets, Didier (thesis director).

Subjects/Keywords: Equations de Schrödinger non-linéaires; Equation de Gross-Pitaevskii; Théorie de scattering; Théorie spectrale; Vortex filament; Schéma semi-discret; Nonlinear Schrödinger equations; Gross-Pitaevskii equation; 510

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Mohamad, H. (2014). Sur l'équation de Gross-Pitaevskii uni-dimensionnelle et quelques généralisations du flot par courbure binormale : On the one-dimensional Gross-Pitaevskii equation and some generalisations of the binormal curvature flow. (Doctoral Dissertation). Université Pierre et Marie Curie – Paris VI. Retrieved from http://www.theses.fr/2014PA066176

Chicago Manual of Style (16^th Edition):

Mohamad, Haidar. “Sur l'équation de Gross-Pitaevskii uni-dimensionnelle et quelques généralisations du flot par courbure binormale : On the one-dimensional Gross-Pitaevskii equation and some generalisations of the binormal curvature flow.” 2014. Doctoral Dissertation, Université Pierre et Marie Curie – Paris VI. Accessed April 14, 2021. http://www.theses.fr/2014PA066176.

MLA Handbook (7^th Edition):

Mohamad, Haidar. “Sur l'équation de Gross-Pitaevskii uni-dimensionnelle et quelques généralisations du flot par courbure binormale : On the one-dimensional Gross-Pitaevskii equation and some generalisations of the binormal curvature flow.” 2014. Web. 14 Apr 2021.

Vancouver:

Mohamad H. Sur l'équation de Gross-Pitaevskii uni-dimensionnelle et quelques généralisations du flot par courbure binormale : On the one-dimensional Gross-Pitaevskii equation and some generalisations of the binormal curvature flow. [Internet] [Doctoral dissertation]. Université Pierre et Marie Curie – Paris VI; 2014. [cited 2021 Apr 14]. Available from: http://www.theses.fr/2014PA066176.

Council of Science Editors:

Mohamad H. Sur l'équation de Gross-Pitaevskii uni-dimensionnelle et quelques généralisations du flot par courbure binormale : On the one-dimensional Gross-Pitaevskii equation and some generalisations of the binormal curvature flow. [Doctoral Dissertation]. Université Pierre et Marie Curie – Paris VI; 2014. Available from: http://www.theses.fr/2014PA066176

NSYSU

4. Liu, Fang-hsin. A continuation algorithm embedded in the radial basis function collocation method for Gross-Pitaevskii equation.

Degree: Master, Applied Mathematics, 2015, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0705115-143616

► We compute the numerical solution of Gross-Pitaevskii equation by a continuation algorithm embedded in the radial basis function collocation method. The equation is interpolated by… (more)

Subjects/Keywords: radial basis function; continuation method; collocation method; Gross-Pitaevskii equation; inverse multiquadric function

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Liu, F. (2015). A continuation algorithm embedded in the radial basis function collocation method for Gross-Pitaevskii equation. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0705115-143616

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Liu, Fang-hsin. “A continuation algorithm embedded in the radial basis function collocation method for Gross-Pitaevskii equation.” 2015. Thesis, NSYSU. Accessed April 14, 2021. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0705115-143616.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Liu, Fang-hsin. “A continuation algorithm embedded in the radial basis function collocation method for Gross-Pitaevskii equation.” 2015. Web. 14 Apr 2021.

Vancouver:

Liu F. A continuation algorithm embedded in the radial basis function collocation method for Gross-Pitaevskii equation. [Internet] [Thesis]. NSYSU; 2015. [cited 2021 Apr 14]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0705115-143616.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Liu F. A continuation algorithm embedded in the radial basis function collocation method for Gross-Pitaevskii equation. [Thesis]. NSYSU; 2015. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0705115-143616

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Indian Institute of Science

5. Shukla, Vishwanath. Particles and Fields in Superfluid Turbulence : Numerical and Theoretical Studies.

Degree: PhD, Faculty of Science, 2017, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/2933

► In this thesis we study a variety of problems in superfluid turbulence, princi-pally in two dimensions. A summary of the main results of our studies… (more)

▼ In this thesis we study a variety of problems in superfluid turbulence, princi-pally in two dimensions. A summary of the main results of our studies is given below; we indicate the Chapters in which we present these. In Chapter 1, we provide an overview of several problems in superfluid turbulence with special emphasis on background material for the problems we study in this thesis. In particular, we give: (a) a brief introduction of fluid turbulence; (b) an overview of superfluidity and the phenomenological two-fluid model; (c) a brief overview of experiments on superfluid turbulence; (d) an introductory accounts of the phenomenological models used in the study of superfluid turbulence. We end with a summary of the problems we study in subsequent Chapters of this thesis. In Chapter 2, we present a systematic, direct numerical simulation of the two-dimensional, Fourier-truncated, Gross-Pitaevskii equation to study the turbulent evolutions of its solutions for a variety of initial conditions and a wide range of parameters. We find that the time evolution of this system can be classified into four regimes with qualitatively different statistical properties. First, there are transients that depend on the initial conditions. In the second regime, power- law scaling regions, in the energy and the occupation-number spectra, appear and start to develop; the exponents of these power laws and the extents of the scaling regions change with time and depend on the initial condition. In the third regime, the spectra drop rapidly for modes with wave numbers k > kc and partial thermalization takes place for modes with k < kc ; the self-truncation wave number kc(t) depends on the initial conditions and it grows either as a power of t or as log t. Finally, in the fourth regime, complete thermalization is achieved and, if we account for finite-size effects carefully, correlation functions and spectra are consistent with their nontrivial Berezinskii-Kosterlitz-Thouless forms. Our work is a natural generalization of recent studies of thermalization in the Euler and other hydrodynamical equations; it combines ideas from fluid dynamics and turbulence, on the one hand, and equilibrium and nonequilibrium statistical mechanics on the other. In Chapter 3, we present the first calculation of the mutual-friction coefficients α and α (which are parameters in the Hall-Vinen-Bekharevich-Khalatnikov two-fluid model that we study in chapter 5) as a function of temperature in a homogeneous Bose gas in two-dimensions by using the Galerkin-truncated Gross-Pitaevskii equation, with very special initial conditions, which we obtain by using the advective, real, Ginzburg-Landau equation (ARGLE) and an equilibration procedure that uses a stochastic Ginzburg-Landau equation (SGLE). We also calculate the normal-fluid density as a function of temperature. In Chapter 4, we elucidate the interplay of particles and fields in superfluids, in both simple and turbulent flows. We carry out extensive direct numerical simulations (DNSs) of this interplay for the… Advisors/Committee Members: Pandit, Rahul (advisor).

Subjects/Keywords: Superfluid Turbulence; Superfluids-Particles and Fields; Fluid Turbulence; Gross-Pitaevskii Equation Turbulence; Hall-Vinen-Bekharevich-Khalatnikov Model; Turbulence; Superfluid Hydrodynamics; Superfluid Mutual-Friction Coefficients; Chaotic Dynamics; Fourier Trunctated Gross Pitaevskii Equation; Galerkin-Trunctated Gross Pitaevskii Equation; Fluid Mechanics; Vortex Dynamics; Physics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Shukla, V. (2017). Particles and Fields in Superfluid Turbulence : Numerical and Theoretical Studies. (Doctoral Dissertation). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/2933

Chicago Manual of Style (16^th Edition):

Shukla, Vishwanath. “Particles and Fields in Superfluid Turbulence : Numerical and Theoretical Studies.” 2017. Doctoral Dissertation, Indian Institute of Science. Accessed April 14, 2021. http://etd.iisc.ac.in/handle/2005/2933.

MLA Handbook (7^th Edition):

Shukla, Vishwanath. “Particles and Fields in Superfluid Turbulence : Numerical and Theoretical Studies.” 2017. Web. 14 Apr 2021.

Vancouver:

Shukla V. Particles and Fields in Superfluid Turbulence : Numerical and Theoretical Studies. [Internet] [Doctoral dissertation]. Indian Institute of Science; 2017. [cited 2021 Apr 14]. Available from: http://etd.iisc.ac.in/handle/2005/2933.

Council of Science Editors:

Shukla V. Particles and Fields in Superfluid Turbulence : Numerical and Theoretical Studies. [Doctoral Dissertation]. Indian Institute of Science; 2017. Available from: http://etd.iisc.ac.in/handle/2005/2933

6. Satarić Bogdan. Paralelno transponovanje podataka u okviru numeričkog algoritma za rešavanje Gros-Pitaevski jednačine.

Degree: 2017, University of Novi Sad

URL: https://www.cris.uns.ac.rs/DownloadFileServlet/Disertacija149276491137025.pdf?controlNumber=(BISIS)104548&fileName=149276491137025.pdf&id=8211&source=OATD&language=en ; https://www.cris.uns.ac.rs/record.jsf?recordId=104548&source=OATD&language=en

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Ova doktorska teza se bavi proučavanjem i razvojem paralelnih algoritama za transponovanje distribuiranih trodimenzionalnih struktura podataka, kao i implementacijom ovih algoritama u okviru C/OpenMP/MPI… (more)

Subjects/Keywords: Paralelno transponovanje podataka, Gros-Pitaevski jednačina, 3D strukturepodataka, Hibridni algoritam; Parallel data transposition, Gross-Pitaevskii equation, 3D data structures, Hybridalghoritm

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Bogdan, S. (2017). Paralelno transponovanje podataka u okviru numeričkog algoritma za rešavanje Gros-Pitaevski jednačine. (Thesis). University of Novi Sad. Retrieved from https://www.cris.uns.ac.rs/DownloadFileServlet/Disertacija149276491137025.pdf?controlNumber=(BISIS)104548&fileName=149276491137025.pdf&id=8211&source=OATD&language=en ; https://www.cris.uns.ac.rs/record.jsf?recordId=104548&source=OATD&language=en

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Bogdan, Satarić. “Paralelno transponovanje podataka u okviru numeričkog algoritma za rešavanje Gros-Pitaevski jednačine.” 2017. Thesis, University of Novi Sad. Accessed April 14, 2021. https://www.cris.uns.ac.rs/DownloadFileServlet/Disertacija149276491137025.pdf?controlNumber=(BISIS)104548&fileName=149276491137025.pdf&id=8211&source=OATD&language=en ; https://www.cris.uns.ac.rs/record.jsf?recordId=104548&source=OATD&language=en.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Bogdan, Satarić. “Paralelno transponovanje podataka u okviru numeričkog algoritma za rešavanje Gros-Pitaevski jednačine.” 2017. Web. 14 Apr 2021.

Vancouver:

Bogdan S. Paralelno transponovanje podataka u okviru numeričkog algoritma za rešavanje Gros-Pitaevski jednačine. [Internet] [Thesis]. University of Novi Sad; 2017. [cited 2021 Apr 14]. Available from: https://www.cris.uns.ac.rs/DownloadFileServlet/Disertacija149276491137025.pdf?controlNumber=(BISIS)104548&fileName=149276491137025.pdf&id=8211&source=OATD&language=en ; https://www.cris.uns.ac.rs/record.jsf?recordId=104548&source=OATD&language=en.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Bogdan S. Paralelno transponovanje podataka u okviru numeričkog algoritma za rešavanje Gros-Pitaevski jednačine. [Thesis]. University of Novi Sad; 2017. Available from: https://www.cris.uns.ac.rs/DownloadFileServlet/Disertacija149276491137025.pdf?controlNumber=(BISIS)104548&fileName=149276491137025.pdf&id=8211&source=OATD&language=en ; https://www.cris.uns.ac.rs/record.jsf?recordId=104548&source=OATD&language=en

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Washington State University

7. [No author]. NONLINEAR PHENOMENA AND STRIPE PHASES IN BOSE-EINSTEIN CONDENSATES .

Degree: 2019, Washington State University

URL: http://hdl.handle.net/2376/17860

► Dilute-gas Bose-Einstein condensates offer a versatile testbed for the investigation of quantum phenomena. On the mean-field level, these ultracold atomic systems are described by the… (more)

▼ Dilute-gas Bose-Einstein condensates offer a versatile testbed for the investigation of quantum phenomena. On the mean-field level, these ultracold atomic systems are described by the Gross-Pitaevskii equation which captures the nonlinearities induced by particle interactions. The analytical simplicity of behavior in the linear regime, i.e. in the absence of interparticle interactions, allows for the study of novel particle dispersions, generation of solid-state analogues, and the construction of atom interferometers. Nonlinearities lead to the formation of additional features such as solitonic matter-waves and dispersion loops. The first two studies in this dissertation investigate strongly nonlinear phenomena in 87Rb Bose-Einstein condensates. The inherently nonlinear matter-wave structures known as solitons have been previously realized in one- and two-component systems, Here, that work is extended to three-component systems where two new species of soliton are observed. The second study considers the effects of interactions in optical lattice systems. Nonlinear behavior in an optical lattice is generally avoided, especially in atom interferometry applications. When nonlinear behavior dominates over the optical lattice potential a novel band loop appears in the lowest band of the dispersion. In this dissertation, Rabi oscillations and Bloch oscillations are observed in condensates in weak optical lattices and the resultant non-adiabatic behavior is discussed. In the final two studies, novel quantum phases are generated by combining spin-orbit (SO) coupling with a second coupling type. For instance, supplementing the SO-coupling with optical lattice assisted hopping between the minima of the SO-coupled dispersion leads to the generation of the SO-coupled stripe phase. This phase is closely related to a supersolid, an exotic state of matter which simultaneously possesses the properties of a superfluid and a crystalline solid. By instead adding a radio-frequency field that also couples two Zeeman sublevels, an emergent lattice is formed which can exhibit Galilean invariant Kapitza-Dirac scattering and Bloch oscillations. Both of these compound coupling schemes are discussed. Advisors/Committee Members: Engels, Peter (advisor).

Subjects/Keywords: Physics; Atomic physics; Condensed matter physics; bloch oscillations; bose-einstein condensates; Gross–Pitaevskii equation; nonlinear dispersions; solitons; spin-orbit coupling

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APA (6^th Edition):

author], [. (2019). NONLINEAR PHENOMENA AND STRIPE PHASES IN BOSE-EINSTEIN CONDENSATES . (Thesis). Washington State University. Retrieved from http://hdl.handle.net/2376/17860

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

author], [No. “NONLINEAR PHENOMENA AND STRIPE PHASES IN BOSE-EINSTEIN CONDENSATES .” 2019. Thesis, Washington State University. Accessed April 14, 2021. http://hdl.handle.net/2376/17860.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

author], [No. “NONLINEAR PHENOMENA AND STRIPE PHASES IN BOSE-EINSTEIN CONDENSATES .” 2019. Web. 14 Apr 2021.

Vancouver:

author] [. NONLINEAR PHENOMENA AND STRIPE PHASES IN BOSE-EINSTEIN CONDENSATES . [Internet] [Thesis]. Washington State University; 2019. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/2376/17860.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

author] [. NONLINEAR PHENOMENA AND STRIPE PHASES IN BOSE-EINSTEIN CONDENSATES . [Thesis]. Washington State University; 2019. Available from: http://hdl.handle.net/2376/17860

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

8. Petrović Nikola. Exact spatiotemporal traveling and solitary wave solutions for the generalized nonlinear Schrödinger equation.

Degree: PhD, Physics, 2013, University of Belgrade

URL: http://dx.doi.org/10.2298/BG20131016PETROVIC ; http://eteze.bg.ac.rs/application/showtheses?thesesId=747 ; https://fedorabg.bg.ac.rs/fedora/get/o:7042/bdef:Content/get ; http://vbs.rs/scripts/cobiss?command=SEARCH&base=99999&select=ID=44721935

► The progress of the field of non-linear optics greatly depends on our ability to find solutions of various differential equations that naturally occur in the… (more)

▼ The progress of the field of non-linear optics greatly depends on our ability to find solutions of various differential equations that naturally occur in the systems where light interacts with nonlinear media. Though re-creating the systems through experiment and performing computer simulations are the two most common and fruitful approaches, the ultimate goal remains to find exact solutions of these systems. The goal of this Thesis is to combine the work done in the field of finding exact solutions to certain classes of non-linear differential Schrödinger equations (NLSE). Most notably, there has been a breakthrough as of late in applying various expansion techniques in finding certain exact solutions to various NLSE. Despite the limitations of combining said solutions due to the non-linear nature of the solutions and the fact that not all solutions can be found using these techniques, the very fact that we can identify certain exact solutions is of tremendous importance to the field, especially when it comes to evaluating the kinds of functions and behavior that are possible within such systems. This Thesis will focus primarily on applying the F-expansion technique using the Jacobi elliptic functions (JEFs) to solve various forms of the NLSE with the cubic nonlinearity. The NLSE with a cubic nonlinearity is one of fundamental importance in the field of nonlinear optics because it describes the travelling of a light wave through a medium with a Kerr-like nonlinearity. Through certain modification of the technique we can find exact solutions in a very large class of systems. The systems I present in this Thesis will share a certain set of common properties. All of the equations I will tackle have a single longitudinal variable, either temporal or spatial, due to the application of the paraxial wave approximation, and up to three transverse dimensions, again both temporal and spatial. If all the transverse variables are spatial I x assign to the sum of their second derivatives a diffraction coefficient β whereas if one of them is temporal, I speak of the diffraction/dispersion coefficient. The two coefficients can be normalized into one, up to their sign. In the case of anomalous dispersion, the two coefficients have the same sign. In the case of normal dispersion, the two coefficients have the opposite signs. Apart from these terms which are present in the ordinary wave equation of linear optics, we also have the third order nonlinearity whose strength is determined by a parameter χ and we also have the term γ which describes the gain of loss of the signal inside our system. The first system I will tackle in the Thesis is the NLSE with a cubic nonlinearity, for both the anomalous and normal dispersion. In the case of the normal dispersion, the symmetry between the temporal and other transverse variables is broken, and a previously unknown ansatz had to be used. I obtained that the solutions for the two systems behave similarly. If one modifies the diffraction and nonlinearity sinusoidally, one can obtain stable…

Subjects/Keywords: Jacobi elliptic function nonlinear Schrödinger equation Gross-Pitaevskii; Jakobijeve eliptične funkcije nelinearna Šredingerova jednačina Gros-Pitaevski

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APA (6^th Edition):

Nikola, P. (2013). Exact spatiotemporal traveling and solitary wave solutions for the generalized nonlinear Schrödinger equation. (Doctoral Dissertation). University of Belgrade. Retrieved from http://dx.doi.org/10.2298/BG20131016PETROVIC ; http://eteze.bg.ac.rs/application/showtheses?thesesId=747 ; https://fedorabg.bg.ac.rs/fedora/get/o:7042/bdef:Content/get ; http://vbs.rs/scripts/cobiss?command=SEARCH&base=99999&select=ID=44721935

Chicago Manual of Style (16^th Edition):

Nikola, Petrović. “Exact spatiotemporal traveling and solitary wave solutions for the generalized nonlinear Schrödinger equation.” 2013. Doctoral Dissertation, University of Belgrade. Accessed April 14, 2021. http://dx.doi.org/10.2298/BG20131016PETROVIC ; http://eteze.bg.ac.rs/application/showtheses?thesesId=747 ; https://fedorabg.bg.ac.rs/fedora/get/o:7042/bdef:Content/get ; http://vbs.rs/scripts/cobiss?command=SEARCH&base=99999&select=ID=44721935.

MLA Handbook (7^th Edition):

Nikola, Petrović. “Exact spatiotemporal traveling and solitary wave solutions for the generalized nonlinear Schrödinger equation.” 2013. Web. 14 Apr 2021.

Vancouver:

Nikola P. Exact spatiotemporal traveling and solitary wave solutions for the generalized nonlinear Schrödinger equation. [Internet] [Doctoral dissertation]. University of Belgrade; 2013. [cited 2021 Apr 14]. Available from: http://dx.doi.org/10.2298/BG20131016PETROVIC ; http://eteze.bg.ac.rs/application/showtheses?thesesId=747 ; https://fedorabg.bg.ac.rs/fedora/get/o:7042/bdef:Content/get ; http://vbs.rs/scripts/cobiss?command=SEARCH&base=99999&select=ID=44721935.

Council of Science Editors:

Nikola P. Exact spatiotemporal traveling and solitary wave solutions for the generalized nonlinear Schrödinger equation. [Doctoral Dissertation]. University of Belgrade; 2013. Available from: http://dx.doi.org/10.2298/BG20131016PETROVIC ; http://eteze.bg.ac.rs/application/showtheses?thesesId=747 ; https://fedorabg.bg.ac.rs/fedora/get/o:7042/bdef:Content/get ; http://vbs.rs/scripts/cobiss?command=SEARCH&base=99999&select=ID=44721935

9. Prat, Tony. Localisation d'Anderson avec des atomes froids : dynamique dans le désordre et perspectives avec des modèles chaotiques : Anderson localization with cold atoms : dynamics in disorder and prospects from chaos.

Degree: Docteur es, Physique, 2017, Université Pierre et Marie Curie – Paris VI

URL: http://www.theses.fr/2017PA066232

►

Dans cette thèse, nous étudions théoriquement plusieurs effets liés à la localisation d'Anderson, dans le contexte des atomes froids. Dans les systèmes d'atomes froids, le… (more)

▼

Dans cette thèse, nous étudions théoriquement plusieurs effets liés à la localisation d'Anderson, dans le contexte des atomes froids. Dans les systèmes d'atomes froids, le désordre est généralement créé à l'aide d'une figure de tavelure optique. Dans la première partie de la thèse, nous discutons des spécificités de ces potentiels optiques, et nous nous intéressons en particulier aux propriétés spectrales. Les expériences usant de l'interaction lumière-matière offrent d'intéressantes possibilités. Dans ce cadre, nous considérons dans une deuxième partie de la thèse l'étalement d'un paquet d'ondes atomique, initialement lancé avec une vitesse non nulle dans un potentiel désordonné. Nous trouvons qu'après un mouvement balistique, le centre de masse du paquet subit une rétro-réflection et retourne lentement à sa position initialle, se comportant comme un boomerang. Nous introduisons ensuite les interactions inter-atomiques dans une troisième partie. Nous considèrons des gaz dilués de bosons condensés, et traitons les interactions au niveau champ moyen. Plusieurs situations sont étudiées numériquement, en particulier le boomerang quantique, et l'étalement dynamique – à la fois en impulsion et en énergie – d'ondes de matière préparées en ondes planes. Dans la dernière partie de la thèse, nous montrons que des modèles chaotiques offrent des perspectives intéressantes pour l'étude de la localisation d'Anderson. D'une part, nous présentons des éléments probants en faveur d'un kick rotor sans spin dans l'ensemble symplectique. D'autre part, le réexamen de modèles communément étudiés de kick rotors quasi-périodiques révèle des résultats intrigants.

This thesis theoretically investigates several effects related to Anderson localization, focusing on the context of disordered and chaotic cold-atomic systems. In cold-atomic systems, optical speckle patterns are often used to create the disorder. The resulting potentials felt by the atoms differ from Gaussian random potentials, commonly assumed in the description of condensed-matter systems. In the first part of the thesis, we discuss their specificities, with an emphasis on the spectral properties. Atom-optics experiments offer interesting possibilities, such as the possibility to directly probe the atoms inside the disordered potential. In view of these possibilities, we consider in the second part of the thesis the spreading of matter wave packets initially launched with a non-zero velocity. We find that after an initial ballistic motion, the packet center-of-mass experiences a retroreflection and slowly returns to its initial position, mimicking a boomerang. Atom-atom interactions are then introduced in a third part. We consider dilute condensed bosonic gases, and treat the interactions at the mean-field (Gross-Pitaevskii) level. Various situations are studied numerically, in particular the quantum boomerang scenario, and the dynamical spreading both in momentum and energy of matter waves prepared as plane waves. In the last part, we show that chaotic models offer…

Advisors/Committee Members: Cherroret, Nicolas (thesis director), Delande, Dominique (thesis director).

Subjects/Keywords: Localisation d'Anderson; Désordre; Potentiel speckle; Onde de matière; Equation de Gross-Pitaevskii; Chaos quantique; Anderson localization; Disorder; Matter wave; 530

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Prat, T. (2017). Localisation d'Anderson avec des atomes froids : dynamique dans le désordre et perspectives avec des modèles chaotiques : Anderson localization with cold atoms : dynamics in disorder and prospects from chaos. (Doctoral Dissertation). Université Pierre et Marie Curie – Paris VI. Retrieved from http://www.theses.fr/2017PA066232

Chicago Manual of Style (16^th Edition):

Prat, Tony. “Localisation d'Anderson avec des atomes froids : dynamique dans le désordre et perspectives avec des modèles chaotiques : Anderson localization with cold atoms : dynamics in disorder and prospects from chaos.” 2017. Doctoral Dissertation, Université Pierre et Marie Curie – Paris VI. Accessed April 14, 2021. http://www.theses.fr/2017PA066232.

MLA Handbook (7^th Edition):

Prat, Tony. “Localisation d'Anderson avec des atomes froids : dynamique dans le désordre et perspectives avec des modèles chaotiques : Anderson localization with cold atoms : dynamics in disorder and prospects from chaos.” 2017. Web. 14 Apr 2021.

Vancouver:

Prat T. Localisation d'Anderson avec des atomes froids : dynamique dans le désordre et perspectives avec des modèles chaotiques : Anderson localization with cold atoms : dynamics in disorder and prospects from chaos. [Internet] [Doctoral dissertation]. Université Pierre et Marie Curie – Paris VI; 2017. [cited 2021 Apr 14]. Available from: http://www.theses.fr/2017PA066232.

Council of Science Editors:

Prat T. Localisation d'Anderson avec des atomes froids : dynamique dans le désordre et perspectives avec des modèles chaotiques : Anderson localization with cold atoms : dynamics in disorder and prospects from chaos. [Doctoral Dissertation]. Université Pierre et Marie Curie – Paris VI; 2017. Available from: http://www.theses.fr/2017PA066232

University of Texas – Austin

10. -6441-921X. The dynamics of bose gases.

Degree: PhD, Mathematics, 2015, University of Texas – Austin

URL: http://hdl.handle.net/2152/31511

► We study the Gross-Pitaevskii (GP) hierarchy, which is an infinite sequence of coupled partial differential equations that models the dynamics of Bose gases and arises… (more)

Subjects/Keywords: Partial differential equations; PDE; Mathematical physics; Gross-Pitaevskii hierarchy; Bose gases; Bosons; Schrodinger equation; Quantum mechanics

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APA (6^th Edition):

-6441-921X. (2015). The dynamics of bose gases. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/31511

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Chicago Manual of Style (16^th Edition):

-6441-921X. “The dynamics of bose gases.” 2015. Doctoral Dissertation, University of Texas – Austin. Accessed April 14, 2021. http://hdl.handle.net/2152/31511.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7^th Edition):

-6441-921X. “The dynamics of bose gases.” 2015. Web. 14 Apr 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-6441-921X. The dynamics of bose gases. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2015. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/2152/31511.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-6441-921X. The dynamics of bose gases. [Doctoral Dissertation]. University of Texas – Austin; 2015. Available from: http://hdl.handle.net/2152/31511

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

11. Congy, Thibault. Fluctuations non-linéaires dans les gaz quantiques à deux composantes : Nonlinear fluctuations in two-component quantum gases.

Degree: Docteur es, Physique, 2017, Université Paris-Saclay (ComUE)

URL: http://www.theses.fr/2017SACLS323

►

Cette thèse est dédiée à l'étude des fluctuations non-linéaires dans les condensats de Bose-Einstein à deux composantes. On présente dans le premier chapitre la dynamique… (more)

▼

Cette thèse est dédiée à l'étude des fluctuations non-linéaires dans les condensats de Bose-Einstein à deux composantes. On présente dans le premier chapitre la dynamique de champ moyen des condensats à deux composantes et les différents phénomènes typiques associés au degré de liberté spinoriel. Dans ce même chapitre, on montre que la dynamique des excitations se sépare en deux modes distincts : un mode dit de densité correspondant au mouvement global des atomes à l'intérieur du condensat et un mode dit de polarisation correspondant à la dynamique relative entre les deux espèces constituant le condensat. Ce calcul est généralisé dans le deuxième chapitre où l'on montre que le mode de polarisation persiste en présence d'un couplage cohérent entre les deux composantes. En particulier on analyse la stabilité modulationnelle du mode en déterminant, à l'aide d'une analyse multi-échelle, la dynamique des excitations non-linéaires. On montre alors que les excitations de polarisation, au contraire des excitations de densité, souffrent d'une instabilité de Benjamin-Feir. Cette instabilité est stabilisée aux grandes impulsions par une résonance onde longue - onde courte. Enfin dans le dernier chapitre, on dérive de façon non-perturbative la dynamique de polarisation proche de la limite de Manakov, dynamique quise révèle être régie par une équation de Landau-Lifshitz sans dissipation. Les équations de Landau-Lifshitz appartiennent à une hiérarchie d'équations intégrables (hiérarchie Ablowitz-Kaup-Newell-Segur) et on étudie les solutions à une phase à l'aide de la méthode d'intégration finite-gap ; on détermine notamment à l'aide de cette méthode un nouveau type de soliton pour les condensats à deux composantes. Finalement, profitant de l'intégrabilité du système, on résout le problème de Riemann à l'aide de la théorie de modulation de Whitham et on montre que les condensats à deux composantes peuvent propager des ondes de raréfaction ainsi que des ondes de choc dispersives ; on décrit notamment la modulation de ces ondes de choc par la propagation d'ondes simples et d'ondes de contact d'invariants de Riemann.

This thesis is devoted to the study of nonlinear fluctuations in two-component Bose-Einstein condensates. In the first chapter we derive the mean field dynamics of two-component condensates and we present the distinctive phenomena associated to the spinorial degree of freedom. In the same chapter, we show that the dynamics of the excitations is divided in two distinct modes: a so-called density mode which corresponds to the global motion of the atoms, and a so-called polarization mode which corresponds to the relative motion between the two species composing the condensate. The computation is generalized in the second chapter in which we demonstrate that the polarization mode remains in presence of a coherent coupling between the two components. In particular we study the modulational stability of the mode and we determine through a multi-scaling analysis the dynamics of non-linear excitations. We show that the…

Advisors/Committee Members: Pavloff, Nicolas (thesis director).

Subjects/Keywords: Excitation non-linéaire; Condensat de Bose-Einstein à deux composantes; Équation de Gross-Pitaevskii; Instabilité modulationnelle; Équation de Landau-Lifshitz; Onde de choc dispersive; Nonlinear excitation; Two-component Bose-Einstein condensate; Gross-Pitaevskii equation; Modulational instability; Landau-Lifshitz equation; Dispersive shockwave

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Congy, T. (2017). Fluctuations non-linéaires dans les gaz quantiques à deux composantes : Nonlinear fluctuations in two-component quantum gases. (Doctoral Dissertation). Université Paris-Saclay (ComUE). Retrieved from http://www.theses.fr/2017SACLS323

Chicago Manual of Style (16^th Edition):

Congy, Thibault. “Fluctuations non-linéaires dans les gaz quantiques à deux composantes : Nonlinear fluctuations in two-component quantum gases.” 2017. Doctoral Dissertation, Université Paris-Saclay (ComUE). Accessed April 14, 2021. http://www.theses.fr/2017SACLS323.

MLA Handbook (7^th Edition):

Congy, Thibault. “Fluctuations non-linéaires dans les gaz quantiques à deux composantes : Nonlinear fluctuations in two-component quantum gases.” 2017. Web. 14 Apr 2021.

Vancouver:

Congy T. Fluctuations non-linéaires dans les gaz quantiques à deux composantes : Nonlinear fluctuations in two-component quantum gases. [Internet] [Doctoral dissertation]. Université Paris-Saclay (ComUE); 2017. [cited 2021 Apr 14]. Available from: http://www.theses.fr/2017SACLS323.

Council of Science Editors:

Congy T. Fluctuations non-linéaires dans les gaz quantiques à deux composantes : Nonlinear fluctuations in two-component quantum gases. [Doctoral Dissertation]. Université Paris-Saclay (ComUE); 2017. Available from: http://www.theses.fr/2017SACLS323

12. ZHANG YANZHI. Mathematical analysis and numerical simulation of Bose-Einstein condensation.

Degree: 2006, National University of Singapore

URL: http://scholarbank.nus.edu.sg/handle/10635/15549

Subjects/Keywords: Bose-Einstein condensation; Gross-Pitaevskii equation; central vortex states; Ginzburg-Landau-Schroeding equation

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APA (6^th Edition):

YANZHI, Z. (2006). Mathematical analysis and numerical simulation of Bose-Einstein condensation. (Thesis). National University of Singapore. Retrieved from http://scholarbank.nus.edu.sg/handle/10635/15549

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

YANZHI, ZHANG. “Mathematical analysis and numerical simulation of Bose-Einstein condensation.” 2006. Thesis, National University of Singapore. Accessed April 14, 2021. http://scholarbank.nus.edu.sg/handle/10635/15549.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

YANZHI, ZHANG. “Mathematical analysis and numerical simulation of Bose-Einstein condensation.” 2006. Web. 14 Apr 2021.

Vancouver:

YANZHI Z. Mathematical analysis and numerical simulation of Bose-Einstein condensation. [Internet] [Thesis]. National University of Singapore; 2006. [cited 2021 Apr 14]. Available from: http://scholarbank.nus.edu.sg/handle/10635/15549.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

YANZHI Z. Mathematical analysis and numerical simulation of Bose-Einstein condensation. [Thesis]. National University of Singapore; 2006. Available from: http://scholarbank.nus.edu.sg/handle/10635/15549

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Vienna

13. Bode, Charlotte Anna. Trapping potentials and numerics for Gross-Pitaevskii type equations.

Degree: 2019, University of Vienna

URL: http://othes.univie.ac.at/59507/

►

Diese Arbeit beschäftigt sich mit numerischen Methoden für das Lösen der Gross-Pitaevskii Gleichung (GPG). Die GPG beschreibt die zeitliche Entwicklung von Bose-Einstein Kondensaten. Im Rahmen… (more)

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Diese Arbeit beschäftigt sich mit numerischen Methoden für das Lösen der Gross-Pitaevskii Gleichung (GPG). Die GPG beschreibt die zeitliche Entwicklung von Bose-Einstein Kondensaten. Im Rahmen dessen werden zwei numerische Methoden eingeführt, die Time Splitting Spectral Methode (TSSM) und die Backward Euler Finite Difference (BEFD) Methode, mit Hilfe derer sowohl Grundzustands- als auch Zeitevolutionsrechnungen durchgeführt werden. Ein besonderes Augenmerk liegt auf der numerischen Analyse eines Box-Potentials. Insbesondere im Hinblick auf die Wahl der räumlichen Auflösung werden verschiedene Parameter eines Box-Potentials untersucht. Außerdem wird eine Methode entwickelt, um die Zeitschritte während der Grundzustandsrechnung zu verkleinern: mit dem Ziel, mit wenig Iterationen besonders genaue Grundzustände zu erreichen. Die Grundidee basiert auf der Halbierung des Zeitschritts, sobald sich die Lösung über einen gewissen Zeitraum nicht mehr signifikant ändert. Am Schluss werden Rechenergebnisse präsentiert, die durch eine MATLAB Implementierung erzeugt und auf einer GPU parallelisiert werden. Dabei werden die numerischen Methoden TSSM und BEFD in einer Dimension auf ihre Ordnungen in Zeit und Raum analysiert. Schließlich werden Anwendungsergebnisse in zwei und drei Dimensionen präsentiert.

The nonlinear Schrödinger equation (NLSE) is a partial differential equation with many applications in quantum physics, nonlinear optics, etc. In this thesis, selected numerical methods to deal with dynamical as well as ground state computations of the nonlinear Schrödinger equation are presented with a special focus on the cubic NLSE, also known as the Gross-Pitaevskii equation (GPE), a standard model for Bose-Einstein Condensates (BECs). For such GPEs, we investigate numerical performance and accuracy of a Time Splitting Spectral Method (TSSM) and a Backward Euler Finite Difference (BEFD) Method. We introduce the physics including the scaling of BECs and present some dynamical properties of GPEs. Then, the mathematical theory of the nonlinear eigenvalue problem, which models stationary states of BECs, is briefly discussed. Furthermore, we examine numerical aspects of finding ground state solutions. In particular, a normalized gradient flow method is provided to obtain ground state solutions by propagating an imaginary time. Once the theory of numerical methods is investigated, an adaptive temporal step size adjustment is established to guarantee a fast and accurate convergence of ground state solutions. A special focus lies on the investigation of different confining potentials and their influence on numerical accuracy. Due to discontinuities arising from box potentials with sharp edges a special numerical treatment is required. A detailed analysis of box potentials and their defining parameters with respect to the required spatial resolution is proposed. We examine the influence of the layer size, the height and the nonlinearity constant on time propagation as well as ground state solutions. Finally, we…

Subjects/Keywords: 31.45 Partielle Differentialgleichungen; 31.76 Numerische Mathematik; 31.80 Angewandte Mathematik; 33.23 Quantenphysik; Gross-Pitaevskii Gleichung / Externes Potential / Box Potential / Harmonischer Oszillator / Grundzustand / Bose-Einstein Kondensate; Gross-Pitaevskii equation / Trapping Potential / Box Potential / Harmonic Oscillator / Time Splitting Spectral Method / Normalized Gradient Flow / Ground State / Bose-Einstein Condensate

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Bode, C. A. (2019). Trapping potentials and numerics for Gross-Pitaevskii type equations. (Thesis). University of Vienna. Retrieved from http://othes.univie.ac.at/59507/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Bode, Charlotte Anna. “Trapping potentials and numerics for Gross-Pitaevskii type equations.” 2019. Thesis, University of Vienna. Accessed April 14, 2021. http://othes.univie.ac.at/59507/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Bode, Charlotte Anna. “Trapping potentials and numerics for Gross-Pitaevskii type equations.” 2019. Web. 14 Apr 2021.

Vancouver:

Bode CA. Trapping potentials and numerics for Gross-Pitaevskii type equations. [Internet] [Thesis]. University of Vienna; 2019. [cited 2021 Apr 14]. Available from: http://othes.univie.ac.at/59507/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Bode CA. Trapping potentials and numerics for Gross-Pitaevskii type equations. [Thesis]. University of Vienna; 2019. Available from: http://othes.univie.ac.at/59507/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

14. Edmir Ravazzi Franco Ramos. Dinâmica das excitações dos modos coerentes topológicos em um condensado de Bose-Einstein.

Degree: 2006, University of São Paulo

URL: http://www.teses.usp.br/teses/disponiveis/76/76131/tde-21092007-092513/

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No presente trabalho, estudamos a possibilidade de se produzir um Condensado de Bose-Einstein em um estado excitado de um potencial confinante. Vimos que, com um… (more)

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No presente trabalho, estudamos a possibilidade de se produzir um Condensado de Bose-Einstein em um estado excitado de um potencial confinante. Vimos que, com um campo externo oscilante, é possível transferir átomos do estado fundamental para um estado excitado qualquer. Se esse campo oscilar próximo da freqüência de transição entre os dois modos, é possível aproximar esse sistema para um de dois níveis. Analisando numericamente a evolução temporal das populações de cada nível, vimos que há oscilações de população do tipo Rabi. Estas oscilações variam de acordo com a forma espacial, a intensidade e com a dessintonia do campo aplicado. Vimos, também, que há a formação de franjas do tipo Ramsey, ao aplicarmos um campo oscilatório com dois pulsos separados. Além disso, definindo um parâmetro de ordem como sendo a diferença entre a média temporal da população de cada estado, é possível caracterizar um tipo de transição de fase no condensado. Estudamos como a forma do campo externo interfere na transição de fase, caracterizada pelo parâmetro de ordem. Obtemos também, um valor crítico do campo no qual ocorre essa transição.

In this work, we have studied the possibility of producing a Bose-Einstein Condensate in an excited state of a confining potential. We have seen that, with a oscillatory external field, it is possible to transfer atoms from the ground state to any excited state. If this field oscillates near the transition frequency between the two modes, it is possible to approximate that system to a two-level system. Analyzing numerically the temporal evolution of population of each level, we have seen there are Rabi-like oscillations of population. This oscillations vary according to the spacial shape, the intensity and the detuning of the applied field. We have also seen there is a Ramsey-like fringes formation, if we apply an oscillatory field with separate two pulses. Moreover, defining an order parameter as being a difference between the population time average of each level, it is possible to characterize a kind of phase transition in the condensate. We have studied how the shape of the external field interferes in the phase transition, characterized by the order parameter. We have also obtained a critical value for the field in which that transition occurs.

Advisors/Committee Members: Vanderlei Salvador Bagnato, Miled Hassan Youssef Moussa, Lauro Tomio.

Subjects/Keywords: Condensado de Bose-Einsten; Equação de Gross-Pitaevskii; Modos coerentes topológicos; Bose-Einstein condensate; Coherent topological modes; Gross-Pitaevskii equation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Ramos, E. R. F. (2006). Dinâmica das excitações dos modos coerentes topológicos em um condensado de Bose-Einstein. (Masters Thesis). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/76/76131/tde-21092007-092513/

Chicago Manual of Style (16^th Edition):

Ramos, Edmir Ravazzi Franco. “Dinâmica das excitações dos modos coerentes topológicos em um condensado de Bose-Einstein.” 2006. Masters Thesis, University of São Paulo. Accessed April 14, 2021. http://www.teses.usp.br/teses/disponiveis/76/76131/tde-21092007-092513/.

MLA Handbook (7^th Edition):

Ramos, Edmir Ravazzi Franco. “Dinâmica das excitações dos modos coerentes topológicos em um condensado de Bose-Einstein.” 2006. Web. 14 Apr 2021.

Vancouver:

Ramos ERF. Dinâmica das excitações dos modos coerentes topológicos em um condensado de Bose-Einstein. [Internet] [Masters thesis]. University of São Paulo; 2006. [cited 2021 Apr 14]. Available from: http://www.teses.usp.br/teses/disponiveis/76/76131/tde-21092007-092513/.

Council of Science Editors:

Ramos ERF. Dinâmica das excitações dos modos coerentes topológicos em um condensado de Bose-Einstein. [Masters Thesis]. University of São Paulo; 2006. Available from: http://www.teses.usp.br/teses/disponiveis/76/76131/tde-21092007-092513/

Université de Lorraine

15. Duboscq, Romain. Analyse et simulation d'équations de Schrödinger déterministes et stochastiques. Applications aux condensats de Bose-Einstein en rotation : Analysis and simulation of deterministic and stochastic Schrödinger equations. Applications to rotating Bose-Einstein condensates.

Degree: Docteur es, Mathématiques, 2013, Université de Lorraine

URL: http://www.theses.fr/2013LORR0198

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Dans cette thèse, nous étudions différents aspects mathématiques et numériques des équations de Gross-Pitaevskii et de Schrödinger non linéaire. Nous commençons (chapitre 1) par introduire… (more)

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Dans cette thèse, nous étudions différents aspects mathématiques et numériques des équations de Gross-Pitaevskii et de Schrödinger non linéaire. Nous commençons (chapitre 1) par introduire différents modèles à partir des systèmes physiques que sont les condensats de Bose-Einstein et les impulsions lumineuses dans les fibres optiques. Cette modélisation conduit aux équations aux dérivées partielles stochastiques suivantes : l'équation de Gross-Pitaevskii stochastique et l'équation de Schrödinger non linéaire avec dispersion aléatoire. Ensuite, dans le second chapitre, nous nous intéressons au problème de l'existence et l'unicité d'une solution de ces équations. On montre notamment que le problème de Cauchy a une solution pour l'équation de Gross-Pitaevskii stochastique avec rotation grâce à la construction de la solution associée au problème. Nous abordons ensuite dans le troisième chapitre le problème du calcul des états stationnaires pour l'équation de Gross-Pitaevskii. Nous développons une méthode pseudo-spectrale de discrétisation du Continuous Normalized Gradient Flow, associée à une résolution itérative préconditionnée des sous-espaces de Krylov. Le quatrième chapitre concerne l'étude de schémas pseudo-spectraux pour la dynamique de l'équation de Gross-Pitaevskii et de Schrödinger non linéaire. On procède à une étude numérique de ces schémas (schéma de splitting de Lie et de Strang, ainsi qu'un schéma de relaxation). De plus, on analyse le schéma de Lie dans le cadre de l'équation de Schrödinger non linéaire avec dispersion aléatoire. Finalement, nous présentons, dans le cinquième chapitre, une boîte à outils Matlab (GPELab) développée dans le but de fournir les méthodes numériques que nous avons étudiées

The aim of this Thesis is to study various mathematical and numerical aspects related to the Gross-Pitaevskii and nonlinear Schrödinger equations. We begin (chapter 1) by introducing a few models starting from the physics of Bose-Einstein condensates and optical fibers. This naturally leads to introducing a stochastic Gross-Pitaevskii equation and a nonlinear Schrödinger equation with random dispersion. Next, in the second chapter, we analyze the existence and uniqueness problem for these two equations. We prove that the Cauchy problem admits a solution for the stochastic Gross-Pitaevskii equation with a rotational term by constructing the solution associated with the linear. The third chapter is concerned with the computation of stationary states for the Gross-Pitaevskii equation. We develop a pseudo-spectral approximation scheme for the Continuous Normalized Gradient Flow formulation, combined with preconditioned Krylov subspace methods. This original approach leads to the robust and efficient computation of ground states for fast rotations and strong nonlinearities. In the fourth chapter, we consider some pseudo-spectral schemes for computing the dynamics of the Gross-Pitaevskii and nonlinear Schrödinger equations. These schemes (the Lie's and Strang's splitting schemes and the relaxation scheme) are…

Advisors/Committee Members: Antoine, Xavier (thesis director), Marty, Renaud (thesis director).

Subjects/Keywords: Équation de Schrödinger; Équations aux dérivées partielles stochastiques; Bose-Einstein; Gross-Pitaevskii; Analyse; Analyse numérique; Étude numérique; Simulation; Toolbox Matlab; Schrödinger equation; Stochastic partial differential équations; Bose-Einstein; Gross-Pitaevskii; Analysis; Numerical analysis; Numerical study; Simulation; Matlab toolbox; 515.3; 530.12

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Duboscq, R. (2013). Analyse et simulation d'équations de Schrödinger déterministes et stochastiques. Applications aux condensats de Bose-Einstein en rotation : Analysis and simulation of deterministic and stochastic Schrödinger equations. Applications to rotating Bose-Einstein condensates. (Doctoral Dissertation). Université de Lorraine. Retrieved from http://www.theses.fr/2013LORR0198

Chicago Manual of Style (16^th Edition):

Duboscq, Romain. “Analyse et simulation d'équations de Schrödinger déterministes et stochastiques. Applications aux condensats de Bose-Einstein en rotation : Analysis and simulation of deterministic and stochastic Schrödinger equations. Applications to rotating Bose-Einstein condensates.” 2013. Doctoral Dissertation, Université de Lorraine. Accessed April 14, 2021. http://www.theses.fr/2013LORR0198.

MLA Handbook (7^th Edition):

Duboscq, Romain. “Analyse et simulation d'équations de Schrödinger déterministes et stochastiques. Applications aux condensats de Bose-Einstein en rotation : Analysis and simulation of deterministic and stochastic Schrödinger equations. Applications to rotating Bose-Einstein condensates.” 2013. Web. 14 Apr 2021.

Vancouver:

Duboscq R. Analyse et simulation d'équations de Schrödinger déterministes et stochastiques. Applications aux condensats de Bose-Einstein en rotation : Analysis and simulation of deterministic and stochastic Schrödinger equations. Applications to rotating Bose-Einstein condensates. [Internet] [Doctoral dissertation]. Université de Lorraine; 2013. [cited 2021 Apr 14]. Available from: http://www.theses.fr/2013LORR0198.

Council of Science Editors:

Duboscq R. Analyse et simulation d'équations de Schrödinger déterministes et stochastiques. Applications aux condensats de Bose-Einstein en rotation : Analysis and simulation of deterministic and stochastic Schrödinger equations. Applications to rotating Bose-Einstein condensates. [Doctoral Dissertation]. Université de Lorraine; 2013. Available from: http://www.theses.fr/2013LORR0198

McMaster University

16. Yan, Zhenbin. Birkhoff Normal Form with Application to Gross Pitaevskii Equation.

Degree: PhD, 2007, McMaster University

URL: http://hdl.handle.net/11375/13991

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L^p is supposed to be L with a superscript lower case 'p.'

This thesis investigates a 1-dimensional Gross-Pitaevskii (GP) equation from the viewpoint… (more)

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L^p is supposed to be L with a superscript lower case 'p.'

This thesis investigates a 1-dimensional Gross-Pitaevskii (GP) equation from the viewpoint of a system of Hamiltonian partial differential equations (PDEs). A theorem on Birkhoff normal forms is a particularly important goal of this study. The resulting system is a perturbed system of a completely resonant system, which we analyze, using several forms of perturbation theory. In chapter two, we study estimates 011 integrals of products of four Hermite functions, which represent coefficients of mode coupling, and play an important role in the proof of the Birkhoff normal form theorem. This is a basic problem, which has a close relationship with a problem of Besicovitch, namely the behavior of the L^p norms of L² -normalized Hermite functions. In chapter three we carefully reconsider the linear Schrodinger equation with a harmonic potential, and we introduce a family of Hilbert spaces for studying the GP equation, which generalize the traditional energy spaces in which one works. One unexpected fact is that these function spaces have a close relationship with the former works for the tempered distributions, in particular the N-representation theory due to B. Simon, and V. Bargmann's theory, which uncovers relationship between the tempered distributions and his function spaces through the so-called Segal-Bargmann transformation. In addition, our function spaces have a nice relationship with the Sobolev spaces. In this chapter, a few other questions regarding these function spaces are discussed. In chapter four the proof of the Birkhoff normal form theorem on spaces we have introduced are provided. The analysis is divided into two cases according to the regularity of the related function space. After proving the Birkhoff normal form theorem, we made an analysis of the impact of the perturbation on the main part of the GP system, which we remark is completel:y resonant.

Doctor of Philosophy (PhD)

Advisors/Committee Members: Craig, Walter, Mathematics.

Subjects/Keywords: Gross-Pitaevskii equation; Hamiltonian partial differential equations; Hermite functions; Mathematics; Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Yan, Z. (2007). Birkhoff Normal Form with Application to Gross Pitaevskii Equation. (Doctoral Dissertation). McMaster University. Retrieved from http://hdl.handle.net/11375/13991

Chicago Manual of Style (16^th Edition):

Yan, Zhenbin. “Birkhoff Normal Form with Application to Gross Pitaevskii Equation.” 2007. Doctoral Dissertation, McMaster University. Accessed April 14, 2021. http://hdl.handle.net/11375/13991.

MLA Handbook (7^th Edition):

Yan, Zhenbin. “Birkhoff Normal Form with Application to Gross Pitaevskii Equation.” 2007. Web. 14 Apr 2021.

Vancouver:

Yan Z. Birkhoff Normal Form with Application to Gross Pitaevskii Equation. [Internet] [Doctoral dissertation]. McMaster University; 2007. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/11375/13991.

Council of Science Editors:

Yan Z. Birkhoff Normal Form with Application to Gross Pitaevskii Equation. [Doctoral Dissertation]. McMaster University; 2007. Available from: http://hdl.handle.net/11375/13991

17. RUAN XINRAN. MATHEMATICAL THEORY AND NUMERICAL METHODS FOR BOSE-EINSTEIN CONDENSATION WITH HIGHER ORDER INTERACTIONS.

Degree: 2017, National University of Singapore

URL: http://scholarbank.nus.edu.sg/handle/10635/135445

Subjects/Keywords: modified Gross-Pitaevskii equation; dimension reduction; ground state; dynamics; fundamental gap; asymptotic approximation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

XINRAN, R. (2017). MATHEMATICAL THEORY AND NUMERICAL METHODS FOR BOSE-EINSTEIN CONDENSATION WITH HIGHER ORDER INTERACTIONS. (Thesis). National University of Singapore. Retrieved from http://scholarbank.nus.edu.sg/handle/10635/135445

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

XINRAN, RUAN. “MATHEMATICAL THEORY AND NUMERICAL METHODS FOR BOSE-EINSTEIN CONDENSATION WITH HIGHER ORDER INTERACTIONS.” 2017. Thesis, National University of Singapore. Accessed April 14, 2021. http://scholarbank.nus.edu.sg/handle/10635/135445.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

XINRAN, RUAN. “MATHEMATICAL THEORY AND NUMERICAL METHODS FOR BOSE-EINSTEIN CONDENSATION WITH HIGHER ORDER INTERACTIONS.” 2017. Web. 14 Apr 2021.

Vancouver:

XINRAN R. MATHEMATICAL THEORY AND NUMERICAL METHODS FOR BOSE-EINSTEIN CONDENSATION WITH HIGHER ORDER INTERACTIONS. [Internet] [Thesis]. National University of Singapore; 2017. [cited 2021 Apr 14]. Available from: http://scholarbank.nus.edu.sg/handle/10635/135445.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

XINRAN R. MATHEMATICAL THEORY AND NUMERICAL METHODS FOR BOSE-EINSTEIN CONDENSATION WITH HIGHER ORDER INTERACTIONS. [Thesis]. National University of Singapore; 2017. Available from: http://scholarbank.nus.edu.sg/handle/10635/135445

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

18. CAI YONGYONG. Mathematical Theory and Numerical Methods for Gross-Pitaevskii Equations and Applications.

Degree: 2011, National University of Singapore

URL: http://scholarbank.nus.edu.sg/handle/10635/30714

Subjects/Keywords: Gross-Pitaevskii equation; Bose-Einstein condensate; ground state; error estimate

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

YONGYONG, C. (2011). Mathematical Theory and Numerical Methods for Gross-Pitaevskii Equations and Applications. (Thesis). National University of Singapore. Retrieved from http://scholarbank.nus.edu.sg/handle/10635/30714

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

YONGYONG, CAI. “Mathematical Theory and Numerical Methods for Gross-Pitaevskii Equations and Applications.” 2011. Thesis, National University of Singapore. Accessed April 14, 2021. http://scholarbank.nus.edu.sg/handle/10635/30714.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

YONGYONG, CAI. “Mathematical Theory and Numerical Methods for Gross-Pitaevskii Equations and Applications.” 2011. Web. 14 Apr 2021.

Vancouver:

YONGYONG C. Mathematical Theory and Numerical Methods for Gross-Pitaevskii Equations and Applications. [Internet] [Thesis]. National University of Singapore; 2011. [cited 2021 Apr 14]. Available from: http://scholarbank.nus.edu.sg/handle/10635/30714.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

YONGYONG C. Mathematical Theory and Numerical Methods for Gross-Pitaevskii Equations and Applications. [Thesis]. National University of Singapore; 2011. Available from: http://scholarbank.nus.edu.sg/handle/10635/30714

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

19. Harper, John Howard. Density Profile of a Quantized Vortex Line in Superfluid Helium-4.

Degree: 1975, North Texas State University

URL: https://digital.library.unt.edu/ark:/67531/metadc500722/

► The density amplitude of an isolated quantum vortex line in superfluid 4He is calculated using a generalized Gross-Pitaevskii (G-P) equation. The generalized G-P equation for… (more)

Subjects/Keywords: density amplitudes; quantum vortex lines; Gross-Pitaevskii equation; Liquid helium.; Vortex-motion.

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APA (6^th Edition):

Harper, J. H. (1975). Density Profile of a Quantized Vortex Line in Superfluid Helium-4. (Thesis). North Texas State University. Retrieved from https://digital.library.unt.edu/ark:/67531/metadc500722/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Harper, John Howard. “Density Profile of a Quantized Vortex Line in Superfluid Helium-4.” 1975. Thesis, North Texas State University. Accessed April 14, 2021. https://digital.library.unt.edu/ark:/67531/metadc500722/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Harper, John Howard. “Density Profile of a Quantized Vortex Line in Superfluid Helium-4.” 1975. Web. 14 Apr 2021.

Vancouver:

Harper JH. Density Profile of a Quantized Vortex Line in Superfluid Helium-4. [Internet] [Thesis]. North Texas State University; 1975. [cited 2021 Apr 14]. Available from: https://digital.library.unt.edu/ark:/67531/metadc500722/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Harper JH. Density Profile of a Quantized Vortex Line in Superfluid Helium-4. [Thesis]. North Texas State University; 1975. Available from: https://digital.library.unt.edu/ark:/67531/metadc500722/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

20. Hedhio Luiz Francisco da Luz. Sistemas não-lineares aplicados a condensados atômicos com interações dependentes do tempo.

Degree: 2008, University of São Paulo

URL: http://www.teses.usp.br/teses/disponiveis/43/43134/tde-09052008-095040/

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No presente trabalho foi estudada a dinâmica de um sistema de muitas partículas no regime de temperaturas ultra-baixas. Realizamos um estudo dinâmico de sistemas condensados… (more)

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No presente trabalho foi estudada a dinâmica de um sistema de muitas partículas no regime de temperaturas ultra-baixas. Realizamos um estudo dinâmico de sistemas condensados bidimensionais em uma rede óptica não-linear em uma direção e também na presença de uma armadilha harmônica assimétrica. Investigamos alguns aspectos sobre a estabilização e propagação de sólitons em condensados de Bose-Einstein. O colapso da função de onda é evitado pela não-linearidade periódica dissipativa, no caso de um meio com campo de fundo positivo (com sistemas atômicos atrativos). A variação adiabática do comprimento de espalhamento de fundo leva a existência de sólitons de onda de matéria metaestáveis. Um sóliton dissipativo pode existir no meio atrativo bidimensional (2D) com uma não-linearidade periódica unidimensional (1D), quando um mecanismo de alimentação atômica é utilizado. Um sóliton estável pode existir no caso de condensados repulsivos, em um campo de fundo negativo, com uma armadilha harmônica em uma direção e uma rede óptica não-linear na outra direção. Os resultados inteiramente numéricos, para a equação de Gross-Pitaevskii 2D, confirmam as simulações da abordagem variacional.

In this work the dynamics of a system of many particles in a ultra-low temperature regime was studied. We performed a dynamic study of two-dimensional condensate systems into a nonlinear optical lattice in one direction and also in the presence of an asymmetrical harmonic trap. We investigated some aspects of the stabilization and spread of solitons in a Bose-Einstein condensate. In the case of positive background field media (with attractive atomic systems), the collapse of the wave-packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in an attractive bidimensional (2D) media with unidimensional (1D) periodic nonlinearity. In the case of repulsive condensates, with a negative background field, a stable soliton may exist when we have an harmonic trap in one direction and a nonlinear optical lattice in the other. Variational approach simulations are confirmed by full numerical results for the 2D Gross-Pitaevskii equation.

Advisors/Committee Members: Lauro Tomio, Marcelo Martinelli, Marcelo Takeshi Yamashita.

Subjects/Keywords: Condensação de Bose-Einstein; Crank-Nicolson; Equação de Gross-Pitaevskii; Simulação numérica.; Sólitons; Bose-Einstein condensation; Crank-Nicolson; Gross-Pitaevskii equation; Numerical simulation.; Solitons

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Luz, H. L. F. d. (2008). Sistemas não-lineares aplicados a condensados atômicos com interações dependentes do tempo. (Masters Thesis). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/43/43134/tde-09052008-095040/

Chicago Manual of Style (16^th Edition):

Luz, Hedhio Luiz Francisco da. “Sistemas não-lineares aplicados a condensados atômicos com interações dependentes do tempo.” 2008. Masters Thesis, University of São Paulo. Accessed April 14, 2021. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-09052008-095040/.

MLA Handbook (7^th Edition):

Luz, Hedhio Luiz Francisco da. “Sistemas não-lineares aplicados a condensados atômicos com interações dependentes do tempo.” 2008. Web. 14 Apr 2021.

Vancouver:

Luz HLFd. Sistemas não-lineares aplicados a condensados atômicos com interações dependentes do tempo. [Internet] [Masters thesis]. University of São Paulo; 2008. [cited 2021 Apr 14]. Available from: http://www.teses.usp.br/teses/disponiveis/43/43134/tde-09052008-095040/.

Council of Science Editors:

Luz HLFd. Sistemas não-lineares aplicados a condensados atômicos com interações dependentes do tempo. [Masters Thesis]. University of São Paulo; 2008. Available from: http://www.teses.usp.br/teses/disponiveis/43/43134/tde-09052008-095040/

21. Brtka, Marijana [UNESP]. Oscilações não-lineares em condensados de Bose-Einstein.

Degree: 2004, Universidade Estadual Paulista (UNESP)

URL: http://hdl.handle.net/11449/102506

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Subjects/Keywords: Bose-Einstein, Gas de; Oscilações não-lineares; Gross-Pitaevskii, Equação de; Dinâmica não-linear; Bose-Einstein condensation; Nonlinear dynamics; Nonlinear oscillations; Gross-Pitaevskii equation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Brtka, M. [. (2004). Oscilações não-lineares em condensados de Bose-Einstein. (Doctoral Dissertation). Universidade Estadual Paulista (UNESP). Retrieved from http://hdl.handle.net/11449/102506

Chicago Manual of Style (16^th Edition):

Brtka, Marijana [UNESP]. “Oscilações não-lineares em condensados de Bose-Einstein.” 2004. Doctoral Dissertation, Universidade Estadual Paulista (UNESP). Accessed April 14, 2021. http://hdl.handle.net/11449/102506.

MLA Handbook (7^th Edition):

Brtka, Marijana [UNESP]. “Oscilações não-lineares em condensados de Bose-Einstein.” 2004. Web. 14 Apr 2021.

Vancouver:

Brtka M[. Oscilações não-lineares em condensados de Bose-Einstein. [Internet] [Doctoral dissertation]. Universidade Estadual Paulista (UNESP); 2004. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/11449/102506.

Council of Science Editors:

Brtka M[. Oscilações não-lineares em condensados de Bose-Einstein. [Doctoral Dissertation]. Universidade Estadual Paulista (UNESP); 2004. Available from: http://hdl.handle.net/11449/102506

22. Gargoubi, Hamis. Modélisation des condensats de polaritons dans les microcavités planaires : Modeling of polariton condensates in planar microcavities.

Degree: Docteur es, Physique, 2016, Montpellier; Faculté des sciences de Bizerte (Tunisie)

URL: http://www.theses.fr/2016MONTT327

►

Les polaritons de microcavité sont des états hybrides lumière-matière à caractère bosonique.Dans les dernières décennies, un grand intérêt a été accordé à leur phase de… (more)

Subjects/Keywords: Polaritons; Condensation de Bose-Einstein; Microcavités; Gross-Pitaevskii; Exciton; Polaritons; Bose -Einstein condensation; Microcavities; Gross-Pitaevskii; Exciton

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Gargoubi, H. (2016). Modélisation des condensats de polaritons dans les microcavités planaires : Modeling of polariton condensates in planar microcavities. (Doctoral Dissertation). Montpellier; Faculté des sciences de Bizerte (Tunisie). Retrieved from http://www.theses.fr/2016MONTT327

Chicago Manual of Style (16^th Edition):

Gargoubi, Hamis. “Modélisation des condensats de polaritons dans les microcavités planaires : Modeling of polariton condensates in planar microcavities.” 2016. Doctoral Dissertation, Montpellier; Faculté des sciences de Bizerte (Tunisie). Accessed April 14, 2021. http://www.theses.fr/2016MONTT327.

MLA Handbook (7^th Edition):

Gargoubi, Hamis. “Modélisation des condensats de polaritons dans les microcavités planaires : Modeling of polariton condensates in planar microcavities.” 2016. Web. 14 Apr 2021.

Vancouver:

Gargoubi H. Modélisation des condensats de polaritons dans les microcavités planaires : Modeling of polariton condensates in planar microcavities. [Internet] [Doctoral dissertation]. Montpellier; Faculté des sciences de Bizerte (Tunisie); 2016. [cited 2021 Apr 14]. Available from: http://www.theses.fr/2016MONTT327.

Council of Science Editors:

Gargoubi H. Modélisation des condensats de polaritons dans les microcavités planaires : Modeling of polariton condensates in planar microcavities. [Doctoral Dissertation]. Montpellier; Faculté des sciences de Bizerte (Tunisie); 2016. Available from: http://www.theses.fr/2016MONTT327

Stellenbosch University

23. Olivier, Carel Petrus. A numerical study of the spectrum of the nonlinear Schrodinger equation.

Degree: Mathematical Sciences, 2008, Stellenbosch University

URL: http://hdl.handle.net/10019.1/1744

►

Thesis (MSc (Mathematical Sciences. Applied Mathematics)) – Stellenbosch University, 2008.

The NLS is a universal equation of the class of nonlinear integrable systems. The aim of… (more)

Subjects/Keywords: Applied mathematics; Gross-Pitaevskii equations

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APA (6^th Edition):

Olivier, C. P. (2008). A numerical study of the spectrum of the nonlinear Schrodinger equation. (Thesis). Stellenbosch University. Retrieved from http://hdl.handle.net/10019.1/1744

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Olivier, Carel Petrus. “A numerical study of the spectrum of the nonlinear Schrodinger equation.” 2008. Thesis, Stellenbosch University. Accessed April 14, 2021. http://hdl.handle.net/10019.1/1744.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Olivier, Carel Petrus. “A numerical study of the spectrum of the nonlinear Schrodinger equation.” 2008. Web. 14 Apr 2021.

Vancouver:

Olivier CP. A numerical study of the spectrum of the nonlinear Schrodinger equation. [Internet] [Thesis]. Stellenbosch University; 2008. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10019.1/1744.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Olivier CP. A numerical study of the spectrum of the nonlinear Schrodinger equation. [Thesis]. Stellenbosch University; 2008. Available from: http://hdl.handle.net/10019.1/1744

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Hong Kong University of Science and Technology

24. Kwan, Wing Fai MATH. Applications and modifications of fast Huygens sweeping methods.

Degree: 2017, Hong Kong University of Science and Technology

URL: http://repository.ust.hk/ir/Record/1783.1-91184 ; https://doi.org/10.14711/thesis-991012564467003412 ; http://repository.ust.hk/ir/bitstream/1783.1-91184/1/th_redirect.html

► In this thesis, we study the fast Huygens sweeping method for Schrödinger equations. We propose a simple backward time marching step to avoid the limitation… (more)

Subjects/Keywords: Differential equations, Partial ; Gross-Pitaevskii equations ; Liquid crystals ; Mathematics

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APA (6^th Edition):

Kwan, W. F. M. (2017). Applications and modifications of fast Huygens sweeping methods. (Thesis). Hong Kong University of Science and Technology. Retrieved from http://repository.ust.hk/ir/Record/1783.1-91184 ; https://doi.org/10.14711/thesis-991012564467003412 ; http://repository.ust.hk/ir/bitstream/1783.1-91184/1/th_redirect.html

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Kwan, Wing Fai MATH. “Applications and modifications of fast Huygens sweeping methods.” 2017. Thesis, Hong Kong University of Science and Technology. Accessed April 14, 2021. http://repository.ust.hk/ir/Record/1783.1-91184 ; https://doi.org/10.14711/thesis-991012564467003412 ; http://repository.ust.hk/ir/bitstream/1783.1-91184/1/th_redirect.html.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Kwan, Wing Fai MATH. “Applications and modifications of fast Huygens sweeping methods.” 2017. Web. 14 Apr 2021.

Vancouver:

Kwan WFM. Applications and modifications of fast Huygens sweeping methods. [Internet] [Thesis]. Hong Kong University of Science and Technology; 2017. [cited 2021 Apr 14]. Available from: http://repository.ust.hk/ir/Record/1783.1-91184 ; https://doi.org/10.14711/thesis-991012564467003412 ; http://repository.ust.hk/ir/bitstream/1783.1-91184/1/th_redirect.html.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Kwan WFM. Applications and modifications of fast Huygens sweeping methods. [Thesis]. Hong Kong University of Science and Technology; 2017. Available from: http://repository.ust.hk/ir/Record/1783.1-91184 ; https://doi.org/10.14711/thesis-991012564467003412 ; http://repository.ust.hk/ir/bitstream/1783.1-91184/1/th_redirect.html

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

25. Silva, Luis Ever Young [UNESP]. Exotic Bose-Einstein condensates: binary mixtures and dipolar gases.

Degree: 2013, Universidade Estadual Paulista (UNESP)

URL: http://hdl.handle.net/11449/102535

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nesta tese estudamos conceitos básicos de um condensado de Bose-Einstein (BEC) e sua extensão para sistemas com propriedades mais exóticas, incluindo misturas de dois componentes, com algumas características interessantes encontradas devido à interação entre espécies, e condensados de átomos com forte momento (magnético) dipolar, nos quais a interação dipolo-dipolo (anisotrópica e de longo-alcance), abre novas possibilidades de pesquisa na procura por desconhecidas e fascinantes características para gases atômicos ultra-frios. Mostramos o modelo de campo-médio para misturas de dois BECs interagindo através do potencial de contato e da interação dipolar de longo-alcance empregando termos não lineares de inter e intra-espécies. Aplicamos este modelo em sistemas binários com diferentes armadilhas em que um deles ou ambos podem ser dipolares. Especificamente, estudamos as características físicas de uma mistura de dois BECs - com e sem interação dipolar -, a formação (e dinâmica) de bright solitons para um BEC dipolar, algumas propriedades interessantes para um BEC dipolar no limite de interação forte, e as características de um BEC dipolar quase-livre vinculado à um outro BEC não dipolar confinado numa armadilha magnética. Apresentamos nossos resultados numéricos usando gráficos de densidade, diagramas de fase, de formação de estruturas nas densidades ou a dinâmica dos sistemas, entre outros. Sempre que possível, nossos resultados serão associados com quantidades usadas em técnicas experimentais através de um tipo específico de átomo, o número de partículas, os valores dos parâmetros de interação, a anisotropia da armadilha ou outras quantidades relacionadas com observáveis experimentais

We described the basic ideas of Bose-Einstein condensation (BEC), and then we focused our study on extensions to more exotic condensates including mixtures of two components, where interesting characteristics are found due to the interspecies interaction, and magnetic dipolar gases, which with their ansiotropic long-range dipolar interaction have opened up new avenues of research into cold atoms, in a quest for novel and fascinating features. In this thesis, we present the mean-field model for the binary BEC interacting two-componente mixtures of dipolar and nondipolar BECs, the formation and dynamics of bright solitons, the strong coupling domain for dipolar BECS, and the features of an untrapped bound dipolar droplet in a trapped nondipolar condensate. Our numerical results are presented in density plots, stability, phase plots, structure formartion in densities, breathing oscillation, and more. However, these solutions, whenever possible, are associated with quantities widely handled in experimental techniques,…

Advisors/Committee Members: Universidade Estadual Paulista (UNESP), Adhikari, Sadhan Kumar [UNESP].

Subjects/Keywords: Condensação de Bose-Einstein; Equações de Gross-Pitaevskii; Bose-Einstein condensation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Silva, L. E. Y. [. (2013). Exotic Bose-Einstein condensates: binary mixtures and dipolar gases. (Doctoral Dissertation). Universidade Estadual Paulista (UNESP). Retrieved from http://hdl.handle.net/11449/102535

Chicago Manual of Style (16^th Edition):

Silva, Luis Ever Young [UNESP]. “Exotic Bose-Einstein condensates: binary mixtures and dipolar gases.” 2013. Doctoral Dissertation, Universidade Estadual Paulista (UNESP). Accessed April 14, 2021. http://hdl.handle.net/11449/102535.

MLA Handbook (7^th Edition):

Silva, Luis Ever Young [UNESP]. “Exotic Bose-Einstein condensates: binary mixtures and dipolar gases.” 2013. Web. 14 Apr 2021.

Vancouver:

Silva LEY[. Exotic Bose-Einstein condensates: binary mixtures and dipolar gases. [Internet] [Doctoral dissertation]. Universidade Estadual Paulista (UNESP); 2013. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/11449/102535.

Council of Science Editors:

Silva LEY[. Exotic Bose-Einstein condensates: binary mixtures and dipolar gases. [Doctoral Dissertation]. Universidade Estadual Paulista (UNESP); 2013. Available from: http://hdl.handle.net/11449/102535

26. Chiquillo Márquez, Emerson Evaristo [UNESP]. Bright solitons in a quasi-one-dimensional dipolar Bose-Einstein condensate.

Degree: 2014, Universidade Estadual Paulista (UNESP)

URL: http://hdl.handle.net/11449/108899

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Os gases atômicos ultrafrios têm proporcionado um importante ambiente no estudo de sistemas quânticos de muitas partículas nas duas últimas décadas. Em 2005, a realização experimental dum condensado de Bose-Einstein de 'INTPOT. 52 Cr' com interação magnética dipolo dipolo inter-atômica abriu a porta para um novo nível na pesquisa de gases quânticos degenerados. Ao contrário da interacção de contacto, esta nova interação é de longo alcance e anisotrópica sendo em parte repulsiva ou atrativa. Na aproximação de campomeio, inicialmente, são introduzidas as principais questões sobre condesados com especial interesse no regime atrativo (a< 0) onde é possível a formação de solitons brilhantes e a existência da instabilidade por colapso além de um certo valor crítico. O estudo é realizado,principalmente,usandoummétodonuméricoeumvariacional. Posteriormente, o condensado de Bose-Einstein dipolar é descrito através da equação não-local de GrossPitaevskii. A partir do cenário não-dipolar, por meio da extensão no método numérico e no método variacional é determinada a formação de solitons brilhantes na equação de Gross-Pitaevskii nos modelos tridimensional e quasi-unidimensional para três diferentes condensados dipolares de relevância experimental, isto é 'INTPOT. 52 Cr', 'INTPOT. 168 Er' e 'INTPOT. 164 Dy'. Grá?cos do potencial químico e a raiz quadrática média (rms) dos solitons são obtidos. Finalmente, estuda-se a dinâmica da colisão de dois solitons brilhantes no modelo dipolar quasi-1D de cada condensado acima

The ultracold atomic gases have provided an important environment for studying quantum many-particle systems in the last two decades. In 2005 the experimental realization of a 'INTPOT. 52 Cr' Bose-Einstein condensate with inter-atomic magnetic dipole dipole interaction opened the door to a new level in the research of degenerate quantum gases. As opposed to the usual contact interaction, this new interaction is long-range and anisotropic being partially repulsive or attractive. In the mean-?eld approximation initially are introduced the main issues about non-dipolar condensates with particular interest in the attractive regime (a< 0) where is possible the formation of bright solitons and the existence of instability by collapse beyond a certain critical value. The study is carried out mainly using a numerical method and a variational one. Later, the dipolar Bose-Einstein condensate is depicted by means of the non-local Gross-Pitaevskii equation. From the non-dipolar scenario by means of the extension in the numerical and the variational method is determined the formation of bright solitons in the GPE in the three-dimensional model and…

Advisors/Committee Members: Universidade Estadual Paulista (UNESP), Adhikari, Sadhan Kumar [UNESP].

Subjects/Keywords: Condensação de Bose-Einstein; Equações de Gross-Pitaevskii

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Chiquillo Márquez, E. E. [. (2014). Bright solitons in a quasi-one-dimensional dipolar Bose-Einstein condensate. (Masters Thesis). Universidade Estadual Paulista (UNESP). Retrieved from http://hdl.handle.net/11449/108899

Chicago Manual of Style (16^th Edition):

Chiquillo Márquez, Emerson Evaristo [UNESP]. “Bright solitons in a quasi-one-dimensional dipolar Bose-Einstein condensate.” 2014. Masters Thesis, Universidade Estadual Paulista (UNESP). Accessed April 14, 2021. http://hdl.handle.net/11449/108899.

MLA Handbook (7^th Edition):

Chiquillo Márquez, Emerson Evaristo [UNESP]. “Bright solitons in a quasi-one-dimensional dipolar Bose-Einstein condensate.” 2014. Web. 14 Apr 2021.

Vancouver:

Chiquillo Márquez EE[. Bright solitons in a quasi-one-dimensional dipolar Bose-Einstein condensate. [Internet] [Masters thesis]. Universidade Estadual Paulista (UNESP); 2014. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/11449/108899.

Council of Science Editors:

Chiquillo Márquez EE[. Bright solitons in a quasi-one-dimensional dipolar Bose-Einstein condensate. [Masters Thesis]. Universidade Estadual Paulista (UNESP); 2014. Available from: http://hdl.handle.net/11449/108899

27. Holz, Sheila Magali [UNESP]. Estabilidade de sistemas condensados com interação atrativa ou repulsiva.

Degree: 2005, Universidade Estadual Paulista (UNESP)

URL: http://hdl.handle.net/11449/91842

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Investigamos as soluções estacionárias e dinâmicas da equação de Gross-Pitaevskii generalizada para sistemas atômicos com um potencial confinante e termos não conservativos associados à dissipação e à alimentação atômica, visando a descrição de condensados de Bose-Einstein. Consideramos os casos de comprimentos de espalhamento negativos (interações atrativas) e positivos (interações repulsivas) entre dois átomos. Verificamos como a variação dos parâmetros associados aos termos não conservativos pode produzir situações de instabilidade resultando no fenômeno conhecido como caos espaço temporal. Por outro lado, verificamos também quais combinações de parâmetros leva a soluções de equilíbrio, tipo solitônica. Nessa pesquisa, utilizando esse modelo de campo médio com uma parametrização conhecida, estudamos as propriedades de tais sistemas para alguns valores dos parâmetros não-conservativos, por meio de métodos numéricos e variacionais.

We investigate the stationary and dynamical solutions of the Gross-Pitaevskii equation extended for atomic systems with confining potential in the presence of nonconservative terms associated to atomic dissipation and feeding, in order to describe Bose-Einstein Condensates. We considered the cases of negative (attractive interaction) and positive (repulsive interaction) two-body lenght. We verified how the variation of the parameters associated to those nonconservative terms could produce instabilities resulting in occurrence of spacetemporal chaos. In other hand, we looked for parameters combinations that give us stable solitonic-like solutions. In this research, by using the mean-field approach with a particular parameterization, we studied the properties of these systems for some values of the nonconservative parameters, by means of numerical and variational methods.

Advisors/Committee Members: Universidade Estadual Paulista (UNESP), Tomio, Lauro [UNESP], Filho, Victo dos Santos [UNESP].

Subjects/Keywords: Bose-Einstein, Gas de; Espalhamento (Fisica); Equação de Gross-Pitaevskii; Dinâmica não-linear; Caos espaço-temporal; Autosóliton; Bose-Einstein condensation; Gross-Pitaevskii equation; Nonlinear dynamics; Space-temporal chaos

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Holz, S. M. [. (2005). Estabilidade de sistemas condensados com interação atrativa ou repulsiva. (Masters Thesis). Universidade Estadual Paulista (UNESP). Retrieved from http://hdl.handle.net/11449/91842

Chicago Manual of Style (16^th Edition):

Holz, Sheila Magali [UNESP]. “Estabilidade de sistemas condensados com interação atrativa ou repulsiva.” 2005. Masters Thesis, Universidade Estadual Paulista (UNESP). Accessed April 14, 2021. http://hdl.handle.net/11449/91842.

MLA Handbook (7^th Edition):

Holz, Sheila Magali [UNESP]. “Estabilidade de sistemas condensados com interação atrativa ou repulsiva.” 2005. Web. 14 Apr 2021.

Vancouver:

Holz SM[. Estabilidade de sistemas condensados com interação atrativa ou repulsiva. [Internet] [Masters thesis]. Universidade Estadual Paulista (UNESP); 2005. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/11449/91842.

Council of Science Editors:

Holz SM[. Estabilidade de sistemas condensados com interação atrativa ou repulsiva. [Masters Thesis]. Universidade Estadual Paulista (UNESP); 2005. Available from: http://hdl.handle.net/11449/91842

28. Karhu, Robin. Targeted Energy Transfer in Bose-Einstein Condensates.

Degree: The Institute of Technology, 2013, Linköping UniversityLinköping University

URL: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-98279

► Targeted Energy Transfer is a resonance phenomenon in coupled anharmonic oscillators. In this thesis we investigate if the concept of Targeted Energy Transfer is… (more)

Subjects/Keywords: Bose-Einstein condensate; Targeted Energy Transfer; Gross-Pitaevskii equation; resonance; anharmonic oscillators

…x29;, (2.36) which is the time-independent Gross-Pitaevskii (GP)… …we review the basic theory. We discuss Hamilton’s equation of motion and action-angle… …substituting this into the Euler-Lagrange equation (2.9) results in ∂L (i = 1, 2… …transformation equation θ= ∂W , ∂I (2.19) where W = W (q, I) (2.20)… …transformation is canonical the equation of motion will be ∂H(I) θ˙ = ∂I (2.21)…

10 more images…

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APA (6^th Edition):

Karhu, R. (2013). Targeted Energy Transfer in Bose-Einstein Condensates. (Thesis). Linköping UniversityLinköping University. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-98279

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Karhu, Robin. “Targeted Energy Transfer in Bose-Einstein Condensates.” 2013. Thesis, Linköping UniversityLinköping University. Accessed April 14, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-98279.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Karhu, Robin. “Targeted Energy Transfer in Bose-Einstein Condensates.” 2013. Web. 14 Apr 2021.

Vancouver:

Karhu R. Targeted Energy Transfer in Bose-Einstein Condensates. [Internet] [Thesis]. Linköping UniversityLinköping University; 2013. [cited 2021 Apr 14]. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-98279.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Karhu R. Targeted Energy Transfer in Bose-Einstein Condensates. [Thesis]. Linköping UniversityLinköping University; 2013. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-98279

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

29. CAO XIAOMENG. Numerical Studies of Rotating Bose-Einstein Condensates via Rotating Lagrangian Coordinates.

Degree: 2012, National University of Singapore

URL: http://scholarbank.nus.edu.sg/handle/10635/35553

Subjects/Keywords: Rotating Bose-Einstein Condensation; Gross-Pitaevskii equation, Angular momentum rotation, Lagrangian transformation, Time-splitting method

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

XIAOMENG, C. (2012). Numerical Studies of Rotating Bose-Einstein Condensates via Rotating Lagrangian Coordinates. (Thesis). National University of Singapore. Retrieved from http://scholarbank.nus.edu.sg/handle/10635/35553

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

XIAOMENG, CAO. “Numerical Studies of Rotating Bose-Einstein Condensates via Rotating Lagrangian Coordinates.” 2012. Thesis, National University of Singapore. Accessed April 14, 2021. http://scholarbank.nus.edu.sg/handle/10635/35553.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

XIAOMENG, CAO. “Numerical Studies of Rotating Bose-Einstein Condensates via Rotating Lagrangian Coordinates.” 2012. Web. 14 Apr 2021.

Vancouver:

XIAOMENG C. Numerical Studies of Rotating Bose-Einstein Condensates via Rotating Lagrangian Coordinates. [Internet] [Thesis]. National University of Singapore; 2012. [cited 2021 Apr 14]. Available from: http://scholarbank.nus.edu.sg/handle/10635/35553.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

XIAOMENG C. Numerical Studies of Rotating Bose-Einstein Condensates via Rotating Lagrangian Coordinates. [Thesis]. National University of Singapore; 2012. Available from: http://scholarbank.nus.edu.sg/handle/10635/35553

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

30. GE YUNYI. Dimension reduction of the Gross-Pitaevskii equation for Bose-Einstein condensates.

Degree: 2005, National University of Singapore

URL: http://scholarbank.nus.edu.sg/handle/10635/14637

Subjects/Keywords: Gross-Pitaevskii equation; Bose-Einstein condensate; Normalized gradient flow; Ground state solution; Dynamics; Dimension reduction

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

YUNYI, G. (2005). Dimension reduction of the Gross-Pitaevskii equation for Bose-Einstein condensates. (Thesis). National University of Singapore. Retrieved from http://scholarbank.nus.edu.sg/handle/10635/14637

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

YUNYI, GE. “Dimension reduction of the Gross-Pitaevskii equation for Bose-Einstein condensates.” 2005. Thesis, National University of Singapore. Accessed April 14, 2021. http://scholarbank.nus.edu.sg/handle/10635/14637.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

YUNYI, GE. “Dimension reduction of the Gross-Pitaevskii equation for Bose-Einstein condensates.” 2005. Web. 14 Apr 2021.

Vancouver:

YUNYI G. Dimension reduction of the Gross-Pitaevskii equation for Bose-Einstein condensates. [Internet] [Thesis]. National University of Singapore; 2005. [cited 2021 Apr 14]. Available from: http://scholarbank.nus.edu.sg/handle/10635/14637.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

YUNYI G. Dimension reduction of the Gross-Pitaevskii equation for Bose-Einstein condensates. [Thesis]. National University of Singapore; 2005. Available from: http://scholarbank.nus.edu.sg/handle/10635/14637

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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