subject:(moyal)

Université Paris-Sud – Paris XI

1. Cagnache, Eric. Aspects différentiels et métriques de la géométrie non commutative : application à la physique : Aspects of the metric and differential noncommutative geometry : application to physics.

Degree: Docteur es, Physique mathématique, 2012, Université Paris-Sud – Paris XI

URL: http://www.theses.fr/2012PA112115

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La géométrie non commutative, du fait qu'elle permet de généraliser des objets géométriques sous forme algébrique, offre des perspectives intéressantes pour réunir la théorie quantique… (more)

Subjects/Keywords: Géométrie non commutative; Triplets spectraux; Espace de Moyal; Tore non commutatif; Distance; Noncommutative geometry; Spectral triples; Moyal space; Noncommutative torus; Distance

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

APA (6^th Edition):

Cagnache, E. (2012). Aspects différentiels et métriques de la géométrie non commutative : application à la physique : Aspects of the metric and differential noncommutative geometry : application to physics. (Doctoral Dissertation). Université Paris-Sud – Paris XI. Retrieved from http://www.theses.fr/2012PA112115

Chicago Manual of Style (16^th Edition):

Cagnache, Eric. “Aspects différentiels et métriques de la géométrie non commutative : application à la physique : Aspects of the metric and differential noncommutative geometry : application to physics.” 2012. Doctoral Dissertation, Université Paris-Sud – Paris XI. Accessed January 26, 2021. http://www.theses.fr/2012PA112115.

MLA Handbook (7^th Edition):

Cagnache, Eric. “Aspects différentiels et métriques de la géométrie non commutative : application à la physique : Aspects of the metric and differential noncommutative geometry : application to physics.” 2012. Web. 26 Jan 2021.

Vancouver:

Cagnache E. Aspects différentiels et métriques de la géométrie non commutative : application à la physique : Aspects of the metric and differential noncommutative geometry : application to physics. [Internet] [Doctoral dissertation]. Université Paris-Sud – Paris XI; 2012. [cited 2021 Jan 26]. Available from: http://www.theses.fr/2012PA112115.

Council of Science Editors:

Cagnache E. Aspects différentiels et métriques de la géométrie non commutative : application à la physique : Aspects of the metric and differential noncommutative geometry : application to physics. [Doctoral Dissertation]. Université Paris-Sud – Paris XI; 2012. Available from: http://www.theses.fr/2012PA112115

Universidade de Brasília

2. Marcio Tavares de Castro. Equações de difusão associadas a séries temporais estocásticas : Kramers-Moyal versus Fokker-Planck.

Degree: 2009, Universidade de Brasília

URL: http://bdtd.bce.unb.br/tedesimplificado/tde_busca/arquivo.php?codArquivo=4853

► Equac~oes de difus~ao s~ao largamente utilizadas na obtenc~ao de propriedades de series temporais estocasticas. O objetivo principal deste trabalho e determinar os processos pelos quais… (more)

Subjects/Keywords: processos estocásticos; equação de difusão; Kramers-Moyal; Fokker-Planck; FISICA

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

APA (6^th Edition):

Castro, M. T. d. (2009). Equações de difusão associadas a séries temporais estocásticas : Kramers-Moyal versus Fokker-Planck. (Thesis). Universidade de Brasília. Retrieved from http://bdtd.bce.unb.br/tedesimplificado/tde_busca/arquivo.php?codArquivo=4853

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):

Castro, Marcio Tavares de. “Equações de difusão associadas a séries temporais estocásticas : Kramers-Moyal versus Fokker-Planck.” 2009. Thesis, Universidade de Brasília. Accessed January 26, 2021. http://bdtd.bce.unb.br/tedesimplificado/tde_busca/arquivo.php?codArquivo=4853.

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

MLA Handbook (7^th Edition):

Castro, Marcio Tavares de. “Equações de difusão associadas a séries temporais estocásticas : Kramers-Moyal versus Fokker-Planck.” 2009. Web. 26 Jan 2021.

Vancouver:

Castro MTd. Equações de difusão associadas a séries temporais estocásticas : Kramers-Moyal versus Fokker-Planck. [Internet] [Thesis]. Universidade de Brasília; 2009. [cited 2021 Jan 26]. Available from: http://bdtd.bce.unb.br/tedesimplificado/tde_busca/arquivo.php?codArquivo=4853.

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

Council of Science Editors:

Castro MTd. Equações de difusão associadas a séries temporais estocásticas : Kramers-Moyal versus Fokker-Planck. [Thesis]. Universidade de Brasília; 2009. Available from: http://bdtd.bce.unb.br/tedesimplificado/tde_busca/arquivo.php?codArquivo=4853

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

3. Adrian, Frank Alan. Exact ensemble dynamics for spike-timing-dependent plasticity.

Degree: MS, 2008, Oregon Health Sciences University

URL: doi:10.6083/M4SQ8XCB ; http://digitalcommons.ohsu.edu/etd/342

Subjects/Keywords: Synapses; Fokker-Planck equation; Hebbian plasticity; synaptic weights; stochastic approaches; Kramers-Moyal expansion

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APA (6^th Edition):

Adrian, F. A. (2008). Exact ensemble dynamics for spike-timing-dependent plasticity. (Thesis). Oregon Health Sciences University. Retrieved from doi:10.6083/M4SQ8XCB ; http://digitalcommons.ohsu.edu/etd/342

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):

Adrian, Frank Alan. “Exact ensemble dynamics for spike-timing-dependent plasticity.” 2008. Thesis, Oregon Health Sciences University. Accessed January 26, 2021. doi:10.6083/M4SQ8XCB ; http://digitalcommons.ohsu.edu/etd/342.

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

MLA Handbook (7^th Edition):

Adrian, Frank Alan. “Exact ensemble dynamics for spike-timing-dependent plasticity.” 2008. Web. 26 Jan 2021.

Vancouver:

Adrian FA. Exact ensemble dynamics for spike-timing-dependent plasticity. [Internet] [Thesis]. Oregon Health Sciences University; 2008. [cited 2021 Jan 26]. Available from: doi:10.6083/M4SQ8XCB ; http://digitalcommons.ohsu.edu/etd/342.

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

Council of Science Editors:

Adrian FA. Exact ensemble dynamics for spike-timing-dependent plasticity. [Thesis]. Oregon Health Sciences University; 2008. Available from: doi:10.6083/M4SQ8XCB ; http://digitalcommons.ohsu.edu/etd/342

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

4. Gao, Li. On quantum Euclidean spaces: Continuous deformation and pseudo-differential operators.

Degree: PhD, Mathematics, 2018, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/101546

► Quantum Euclidean spaces are noncommutative deformations of Euclidean spaces. They are prototypes of locally compact noncommutative manifolds in Noncommutative Geometry. In this thesis, we study… (more)

Subjects/Keywords: Noncommutative Euclidean spaces; Moyal Deformation; Pseudo-differential operators

…the parameter h, h being a deformation parameter. The Moyal product, depending gives a… …x5D;. In the rst part of this thesis, we study the continuity of Moyal deformation, or more… …space, which are called Moyal planes as in [15]. Because of its motivation from… …equivalent to the Moyal θ, −d Z Z λθ (f )λθ (g) = λθ (f ?θ g)… …x29; Rd Rd 7 The Moyal product is bilinear, associative and reversed under complex…

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

APA (6^th Edition):

Gao, L. (2018). On quantum Euclidean spaces: Continuous deformation and pseudo-differential operators. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/101546

Chicago Manual of Style (16^th Edition):

Gao, Li. “On quantum Euclidean spaces: Continuous deformation and pseudo-differential operators.” 2018. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed January 26, 2021. http://hdl.handle.net/2142/101546.

MLA Handbook (7^th Edition):

Gao, Li. “On quantum Euclidean spaces: Continuous deformation and pseudo-differential operators.” 2018. Web. 26 Jan 2021.

Vancouver:

Gao L. On quantum Euclidean spaces: Continuous deformation and pseudo-differential operators. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2018. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/2142/101546.

Council of Science Editors:

Gao L. On quantum Euclidean spaces: Continuous deformation and pseudo-differential operators. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/101546

5. Oliva, Maxime. The quantum Wigner current : a geometric approach to quantum dynamics in phase space.

Degree: PhD, 2019, University of Hertfordshire

URL: http://hdl.handle.net/2299/22363

► Phase space is the unity of position and momentum configuration space. It allows for an effective description of dynamical systems and is particularly useful when… (more)

▼ Phase space is the unity of position and momentum configuration space. It allows for an effective description of dynamical systems and is particularly useful when it comes to studying chaos theory and statistical mechanics. After the advent of quantum physics early in the 20th century, E. Wigner [91], J. E. Moyal [62] and H. J. Groenewold [31] introduce a quantum theory in phase space. Despite the apparent added complexity of the mathematics involved in this new framework, the underlying classical and quantum equations show many similarities. The probability distribution in classical physics becomes the Wigner distribution, a probability distribution usually featuring negative values. In 2013, O. Steuernagel and D. Kakofengitis, inspired by the work of H. Bauke [7] and E. Wigner [91], identified the quantum analogue of the classical phase space flow: the Wigner current J [83]. This Wigner current allows the visualisation of quantum dynamics through a quantum fluid dynamics perspective in phase space. This thesis is written by collection of five articles. They are prefaced by an introduction into the basics of quantum phase space theory and its link with both classical phase space dynamics and the standard Schrödinger approach, followed by the articles published during this PhD. Article 1 shows the importance of the integral form of the Wigner current. We use it to derive the Ehrenfest’s theorem, as well as to refute some propositions made within the community. Article 2 shows that, using the Wigner current, an Eulerian and Lagrangian point of view do not always give the same results for the quantum case. We demonstrate that the negativities of the Wigner distribution, sign of quantumness of the system, are created by the Wigner velocity field singularities. The Wigner velocity field is the quantum analogue of the classical phase space velocity field. In Article 3, we see that even though Wigner distributions of quantum systems feature spotty structures which saturate on scales ɑZ [97], the construction of a superoscillating Wigner distribution allows one to generate much smaller structures, of the order of ɑZ /α with α a positive constant potentially very large. In Article 4, we introduce the concept of quantum shear suppression in phase space. The Wigner current features an effective quantum “viscosity”, suppressing classical dynamics fine details. This viscosity is the mechanism by which the Zurek scale is enforced dynamically onto the state in phase space. In Article 5, we apply the previous ideas to Kerr-type oscillators. Its Wigner current is derived, and using it we show that its values are conserved on a ring during the time evolution of the Kerr oscillator. The shear suppression is also studied.

Subjects/Keywords: Quantum; phase; space; theory; theoretical; physics; superoscillations; schrodinger; wigner; function; distribution; negative; probability; viscosity; fluid; mechanics; stagnation; topology; integral; moyal; groenewold; oliva; steuernagel; kakofengitis; feynman; Zurek; Planck; Structures; Scale; trajectory

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

APA (6^th Edition):

Oliva, M. (2019). The quantum Wigner current : a geometric approach to quantum dynamics in phase space. (Doctoral Dissertation). University of Hertfordshire. Retrieved from http://hdl.handle.net/2299/22363

Chicago Manual of Style (16^th Edition):

Oliva, Maxime. “The quantum Wigner current : a geometric approach to quantum dynamics in phase space.” 2019. Doctoral Dissertation, University of Hertfordshire. Accessed January 26, 2021. http://hdl.handle.net/2299/22363.

MLA Handbook (7^th Edition):

Oliva, Maxime. “The quantum Wigner current : a geometric approach to quantum dynamics in phase space.” 2019. Web. 26 Jan 2021.

Vancouver:

Oliva M. The quantum Wigner current : a geometric approach to quantum dynamics in phase space. [Internet] [Doctoral dissertation]. University of Hertfordshire; 2019. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/2299/22363.

Council of Science Editors:

Oliva M. The quantum Wigner current : a geometric approach to quantum dynamics in phase space. [Doctoral Dissertation]. University of Hertfordshire; 2019. Available from: http://hdl.handle.net/2299/22363

6. Oliva, Maxime. The quantum Wigner current : a geometric approach to quantum dynamics in phase space.

Degree: PhD, 2019, University of Hertfordshire

URL: https://doi.org/10.18745/th.22363 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.802947

► Phase space is the unity of position and momentum configuration space. It allows for an effective description of dynamical systems and is particularly useful when… (more)

▼ Phase space is the unity of position and momentum configuration space. It allows for an effective description of dynamical systems and is particularly useful when it comes to studying chaos theory and statistical mechanics. After the advent of quantum physics early in the 20th century, E. Wigner [91], J. E. Moyal [62] and H. J. Groenewold [31] introduce a quantum theory in phase space. Despite the apparent added complexity of the mathematics involved in this new framework, the underlying classical and quantum equations show many similarities. The probability distribution in classical physics becomes the Wigner distribution, a probability distribution usually featuring negative values. In 2013, O. Steuernagel and D. Kakofengitis, inspired by the work of H. Bauke [7] and E. Wigner [91], identified the quantum analogue of the classical phase space flow: the Wigner current J [83]. This Wigner current allows the visualisation of quantum dynamics through a quantum fluid dynamics perspective in phase space. This thesis is written by collection of five articles. They are prefaced by an introduction into the basics of quantum phase space theory and its link with both classical phase space dynamics and the standard Schrödinger approach, followed by the articles published during this PhD. Article 1 shows the importance of the integral form of the Wigner current. We use it to derive the Ehrenfest’s theorem, as well as to refute some propositions made within the community. Article 2 shows that, using the Wigner current, an Eulerian and Lagrangian point of view do not always give the same results for the quantum case. We demonstrate that the negativities of the Wigner distribution, sign of quantumness of the system, are created by the Wigner velocity field singularities. The Wigner velocity field is the quantum analogue of the classical phase space velocity field. In Article 3, we see that even though Wigner distributions of quantum systems feature spotty structures which saturate on scales ɑZ [97], the construction of a superoscillating Wigner distribution allows one to generate much smaller structures, of the order of ɑZ /α with α a positive constant potentially very large. In Article 4, we introduce the concept of quantum shear suppression in phase space. The Wigner current features an effective quantum “viscosity”, suppressing classical dynamics fine details. This viscosity is the mechanism by which the Zurek scale is enforced dynamically onto the state in phase space. In Article 5, we apply the previous ideas to Kerr-type oscillators. Its Wigner current is derived, and using it we show that its values are conserved on a ring during the time evolution of the Kerr oscillator. The shear suppression is also studied.

Subjects/Keywords: Quantum; phase; space; theory; theoretical; physics; superoscillations; schrodinger; wigner; function; distribution; negative; probability; viscosity; fluid; mechanics; stagnation; topology; integral; moyal; groenewold; oliva; steuernagel; kakofengitis; feynman; Zurek; Planck; Structures; Scale; trajectory

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

APA (6^th Edition):

Oliva, M. (2019). The quantum Wigner current : a geometric approach to quantum dynamics in phase space. (Doctoral Dissertation). University of Hertfordshire. Retrieved from https://doi.org/10.18745/th.22363 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.802947

Chicago Manual of Style (16^th Edition):

Oliva, Maxime. “The quantum Wigner current : a geometric approach to quantum dynamics in phase space.” 2019. Doctoral Dissertation, University of Hertfordshire. Accessed January 26, 2021. https://doi.org/10.18745/th.22363 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.802947.

MLA Handbook (7^th Edition):

Oliva, Maxime. “The quantum Wigner current : a geometric approach to quantum dynamics in phase space.” 2019. Web. 26 Jan 2021.

Vancouver:

Oliva M. The quantum Wigner current : a geometric approach to quantum dynamics in phase space. [Internet] [Doctoral dissertation]. University of Hertfordshire; 2019. [cited 2021 Jan 26]. Available from: https://doi.org/10.18745/th.22363 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.802947.

Council of Science Editors:

Oliva M. The quantum Wigner current : a geometric approach to quantum dynamics in phase space. [Doctoral Dissertation]. University of Hertfordshire; 2019. Available from: https://doi.org/10.18745/th.22363 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.802947

University of Bradford

7. Agyo, Sanfo David. Bi-fractional transforms in phase space.

Degree: PhD, 2016, University of Bradford

URL: http://hdl.handle.net/10454/14522

► The displacement operator is related to the displaced parity operator through a two dimensional Fourier transform. Both operators are important operators in phase space and… (more)

Subjects/Keywords: 515; Phase space methods; Coherent states; Bi-fractional coherent states; Bi-fractional Wigner function; Bi-fractional P-function; Bi-fractional Q-function; Bi-fractional Moyal star product; Bi-fractional Berezin formalism

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

APA (6^th Edition):

Agyo, S. D. (2016). Bi-fractional transforms in phase space. (Doctoral Dissertation). University of Bradford. Retrieved from http://hdl.handle.net/10454/14522

Chicago Manual of Style (16^th Edition):

Agyo, Sanfo David. “Bi-fractional transforms in phase space.” 2016. Doctoral Dissertation, University of Bradford. Accessed January 26, 2021. http://hdl.handle.net/10454/14522.

MLA Handbook (7^th Edition):

Agyo, Sanfo David. “Bi-fractional transforms in phase space.” 2016. Web. 26 Jan 2021.

Vancouver:

Agyo SD. Bi-fractional transforms in phase space. [Internet] [Doctoral dissertation]. University of Bradford; 2016. [cited 2021 Jan 26]. Available from: http://hdl.handle.net/10454/14522.

Council of Science Editors:

Agyo SD. Bi-fractional transforms in phase space. [Doctoral Dissertation]. University of Bradford; 2016. Available from: http://hdl.handle.net/10454/14522

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