Semiclassical theory for universality in quantum chaos with symmetry crossover

Keiji Saito, Taro Nagao, Sebastian Müller, Petr Braun

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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.

Original languageEnglish
Article number495101
JournalJournal of Physics A: Mathematical and Theoretical
Issue number49
Publication statusPublished - 2009
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


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