PT -symmetry breaking and universal spectral statistics in quantum kicked rotors

TL;DR

This paper explores PT-symmetry breaking and spectral statistics in a quantum kicked rotor, revealing how non-Hermitian parameters influence phase transitions and spectral distributions in localized and delocalized regimes.

Contribution

It demonstrates the conditions under which PT symmetry is broken or preserved in quantum kicked rotors and analyzes spectral statistics transitions in non-Hermitian regimes.

Findings

PT symmetry breaking occurs with increasing non-Hermitian parameter in localized regimes.

Spectral statistics transition from Wigner-Dyson to Poisson with increasing non-Hermitian parameter.

Spectral distributions follow non-Hermitian random matrix ensemble predictions depending on symmetry classes.

Abstract

We investigate the spontaneous parity-time (PT )-symmetry breaking and spectral properties of a PT symmetric quantum kicked rotor under resonance conditions. At resonance, the QKR reduces to a finite-dimensional system. In the localized regime, we find that increasing the non-Hermitian parameter always induces a transition from a phase where the states exhibit PT symmetry to one where PT symmetry is spontaneously broken. In contrast, in the delocalized regime, the existence of such a transition depends on whether the reduced system is PT symmetric. If the reduced system is not PT symmetric, PT symmetry remains in the broken phase regardless of the non-Hermitian parameter. We further analyze the spectral statistics of the system in the delocalized regime. For real energy spectra, the level-spacing distribution transitions from Wigner-Dyson statistics, associated with the Gaussian orthogonal ensemble, to Poisson statistics as the non-Hermitian parameter increases, with the intermediate regime well described by the Brody distribution. For complex spectra, the level-spacing ratios and distributions are governed by time-reversal symmetry. The spectral statistics align with predictions for non-Hermitian random matrix ensembles in classes AI{\dag} and A, depending on the presence or absence of time-reversal symmetry. Our results provide insights into the spectral characteristics of non-Hermitian quantum chaotic systems and their connection to PT symmetry.