Crossover Driven by Time-reversal Symmetry Breaking in Quantum Chaos

TL;DR

This paper derives exact analytical expressions for the parametric correlations of energy spectra in quantum chaotic systems undergoing symmetry-breaking crossovers, revealing non-Gaussian velocity distributions.

Contribution

It provides the first exact analytical results for parametric spectral correlations during orthogonal-unitary and symplectic-unitary crossovers using the supermatrix method.

Findings

Exact formulas for two-point autocorrelation functions derived.

Velocity distributions in the crossover deviate from Gaussian.

Results enhance understanding of symmetry-breaking effects in quantum chaos.

Abstract

Parametric correlations of energy spectra of quantum chaotic systems are presented in the orthogonal-unitary and symplectic-unitary crossover region. The spectra are allowed to disperse as a function of two external perturbations: one of which preserves time-reversal symmetry, while the other violates it. Exact analytical expressions for the parametric two-point autocorrelation function of the density of states are derived in the crossover region by means of the supermatrix method. For the orthogonal-unitary crossover, the velocity distributions is determined and shown to deviate from Gaussian.