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Philipps-Universität Marburg

1. Rehemanjiang, Aimaiti. Microwave Experiments on Graphs Simulating Spin-1/2 System.

Degree: PhD, Fachbereich Physik, 2018, Philipps-Universität Marburg

URL: http://archiv.ub.uni-marburg.de/diss/z2018/0247

In this work I study the
statistical properties of the Gaussian symplectic ensemble
(GSE) by means of microwave experiments on quantum graphs
mimicking spin-1/2 systems. Additionally, the transport
property of three terminal microwave graphs with orthogonal,
unitary and symplectic symmetry is investigated. In the first
part of this thesis, following the spirit of the idea
proposed by Joyner et al. we construct microwave quantum
graphs to realize a antiunitary symmetry T that squares to
minus one, T^{2} = -1. This symmetry induces degenerate
eigenvalues, which are called Kramers doublets. If the
classical dynamics of the system is chaotic, statistical
features of the spectrum can be well described by the
corresponding statistics of random matrix Gaussian symplectic
ensemble. Indeed, Kramers doublets are observed in reflection
spectrum as expected from the scattering properties of a
symplectic graph. The level spacing distribution of these
doublets is compared with the corresponding random matrix
predictions. Since the level spacing distribution accounts
for the short range eigenvalue correlation, to study the
spectral long range correlation the spectral two point
correlation function and its Fourier transform, the spectral
form factor are analyzed. In order to further examine the
fluctuation of the eigenvalues smoothed quantities such as
number variance and spectral rigidity are discussed. The
graphs used in the experiment consist of two subgraphs
coupled via one pair of connecting bonds. Theoretical study
shows that the level spacing distribution for graphs with one
pair of connecting bonds deviates by few percents from the
random matrix prediction. This difference is too small to be
resolved in the experiment. The one pair of bonds
approximation is introduced to better understand the
symplectic graph we used in the experiment. This model is
extended to address more general cases of the symplectic
graph. Finally, the parameter dependent dynamical transition
of the statistical features of the spectrum from GSE via
Gaussian unitary ensemble (GUE) to Gaussian orthogonal
ensemble (GOE) is studied. In the second part of this thesis,
the collaborative work with Dr. A. M. Martínez- Argüello from
Mexico is briefly presented. A three terminal setup is
proposed to study the universal transport properties of
systems with orthogonal, unitary and symplectic symmetry. The
probability distribution for a transport related quantity is
predicted analytically and microwave graphs are constructed
to test this prediction. The absorption within the system is
modeled by effective Hamiltonian approach. The parameters of
the absorption and coupling are extracted from the
experimental autocorrelation function. This allowed a
comparison between experiment and…
*Advisors/Committee Members: Kuhl, Ulrich (advisor).*

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APA (6^{th} Edition):

Rehemanjiang, A. (2018). Microwave Experiments on Graphs Simulating Spin-1/2 System. (Doctoral Dissertation). Philipps-Universität Marburg. Retrieved from http://archiv.ub.uni-marburg.de/diss/z2018/0247

Chicago Manual of Style (16^{th} Edition):

Rehemanjiang, Aimaiti. “Microwave Experiments on Graphs Simulating Spin-1/2 System.” 2018. Doctoral Dissertation, Philipps-Universität Marburg. Accessed October 19, 2018. http://archiv.ub.uni-marburg.de/diss/z2018/0247.

MLA Handbook (7^{th} Edition):

Rehemanjiang, Aimaiti. “Microwave Experiments on Graphs Simulating Spin-1/2 System.” 2018. Web. 19 Oct 2018.

Vancouver:

Rehemanjiang A. Microwave Experiments on Graphs Simulating Spin-1/2 System. [Internet] [Doctoral dissertation]. Philipps-Universität Marburg; 2018. [cited 2018 Oct 19]. Available from: http://archiv.ub.uni-marburg.de/diss/z2018/0247.

Council of Science Editors:

Rehemanjiang A. Microwave Experiments on Graphs Simulating Spin-1/2 System. [Doctoral Dissertation]. Philipps-Universität Marburg; 2018. Available from: http://archiv.ub.uni-marburg.de/diss/z2018/0247