Universal spectral statistics in Wigner-Dyson, chiral and Andreev star graphs I: construction and numerical results

Abstract

In a series of two papers we investigate the universal spectral statistics of chaotic quantum systems in the ten known symmetry classes of quantum mechanics. In this first paper we focus on the construction of appropriate ensembles of star graphs in the ten symmetry classes. A generalization of the Bohigas-Giannoni-Schmit conjecture is given that covers all these symmetry classes. The conjecture is supported by numerical results that demonstrate the fidelity of the spectral statistics of star graphs to the corresponding Gaussian random-matrix theories.

arXiv comment15 pages

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• Universal Spin Hall Conductance Fluctuations in Chaotic Dirac Quantum Dots
• Scaling behaviour in random non-commutative geometries
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• A Lévy flight for electrons in graphene: superdiffusive-to-diffusive transport transition
• Spin-to-Charge Conversion in 2D Electron Gas and Single-layer Graphene Devices
• Lévy flight for electrons in graphene in the presence of regions with enhanced spin-orbit coupling
• The Ergodicity Landscape of Quantum Theories
• Semiclassical limits for the QCD Dirac operator
• Unorientable topological gravity and orthogonal random matrix universality
• Chaos and moduli space volumes in unorientable JT gravity