Berlin 2018 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 69: Poster: Quantum Systems

DY 69.7: Poster

Donnerstag, 15. März 2018, 15:30–18:00, Poster A

GOE-GUE-Poisson crossover in the nearest neighbor spacing distribution of magnetoexcitons — Frank Schweiner, •Patric Rommel, Jeanine Laturner, Jörg Main, and Günter Wunner — Institut für Theoretische Physik 1, University of Stuttgart, Germany

Until now only for specific transitions between Poissonian statistics (P), the statistics of a Gaussian orthogonal ensemble (GOE), or the statistics of a Gaussian unitary ensemble (GUE) analytical formulas for the level spacing distribution function have been derived within random matrix theory. We investigate arbitrary transitions in the crossover between all three statistics. To this aim we propose a fitting formula for the level spacing distribution function depending on two parameters [1]. Recent investigations on the Hamiltonian of excitons revealed that the combined presence of a cubic band structure and external fields breaks all antiunitary symmetries, and thus the nearest-neighbor spacing distribution of magnetoexcitons can exhibit all three statistics depending on the system parameters. Evaluating the numerical results for magnetoexcitons in dependence on the excitation energy and on a parameter connected with the cubic valence band structure and comparing the results with the formula proposed allows us to investigate the level spacing dynamics in the crossover regime and to distinguish between regular and chaotic behavior as well as between existing or broken antiunitary symmetries. We also investigate the effect of the exciton-phonon interaction on the level statistics [2].

[1] F. Schweiner et al., Phys. Rev. E 96, 052217 (2017).

[2] F. Schweiner et al., Phys. Rev. B 96, 035207 (2017).