Semiclassical theory for universality in quantum chaos with symmetry crossover

Keiji Saitou, Taro Nagao, Sebastian Müller, Petr Braun

Research output: Contribution to journalArticle

6 Citations (Scopus)

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.

Original languageEnglish
Article number495101
JournalJournal of Physics A: Mathematical and Theoretical
Volume42
Issue number49
DOIs
Publication statusPublished - 2009
Externally publishedYes

Fingerprint

Quantum Chaos
Nonlinear sigma Model
Random Matrix Theory
Chaotic systems
matrix theory
Chaos theory
Chaotic System
Periodic Orbits
Universality
Crossover
chaos
crossovers
Orbits
Ensemble
spectral correlation
orbits
Symmetry
Crystal symmetry
symmetry
Term

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Modelling and Simulation
  • Statistics and Probability

Cite this

Semiclassical theory for universality in quantum chaos with symmetry crossover. / Saitou, Keiji; Nagao, Taro; Müller, Sebastian; Braun, Petr.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 42, No. 49, 495101, 2009.

Research output: Contribution to journalArticle

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