Semiclassical Theory for Universality in Quantum Chaos with Symmetry Crossover

Abstract

We address the quantum-classical correspondence for chaotic systems with a crossover between symmetry classes. We consider the energy level statistics of a classically chaotic system in a weak magnetic field. The generating function of spectral correlations is calculated by using the semiclassical periodic-orbit theory. An explicit calculation up to the second order, including the non-oscillatory and oscillatory terms, agrees with the prediction of random matrix theory. Formal expressions of the higher order terms are also presented. The nonlinear sigma (NLS) model of random matrix theory, in the variant of the Bosonic replica trick, is also analyzed for the crossover between the Gaussian orthogonal ensemble and Gaussian unitary ensemble. The diagrammatic expansion of the NLS model is interpreted in terms of the periodic orbit theory.

25 pages, 4 figures, 1 table

References in corpus (9)

• Semiclassical Foundation of Universality in Quantum Chaos
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• Periodic-Orbit Theory of Level Correlations
• Periodic-orbit theory of universal level correlations in quantum chaos
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• Semiclassical Theory for Universality in Quantum Chaos with Symmetry Crossover
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Cited by in corpus (7)

• Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
• Many-body quantum chaos: Analytic connection to random matrix theory
• Distribution of the Ratio of Consecutive Level Spacings for Different Symmetries and Degrees of Chaos
• Statistics of the Spectral Form Factor in the Self-Dual Kicked Ising Model
• Semiclassical Theory for Universality in Quantum Chaos with Symmetry Crossover
• Universality crossover between chiral random matrix ensembles and twisted SU(2) lattice Dirac spectra
• Individual eigenvalue distributions of crossover chiral random matrices and low-energy constants of SU(2)$\times$U(1) lattice gauge theory