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

• URL: http://arxiv.org/abs/2502.20071v2
• Date: Fri, 28 Feb 2025 02:27:27 GMT
• Title: PT -symmetry breaking and universal spectral statistics in quantum kicked rotors
• Authors: Guang Li, Fuxing Chen, Ping Fang,
• Abstract summary: We investigate the spontaneous parity-time breaking and spectral properties of a PT symmetric quantum kicked rotor under resonance conditions.<n>In the localized regime, we find that increasing the non-Hermitian parameter always induces a transition from a phase where PT symmetry is spontaneously broken.<n>In the delocalized regime, the existence of such a transition depends on whether the reduced system is PT symmetric.
• Score: 3.4370223589898266
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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