PT -symmetry breaking and universal spectral statistics in quantum kicked rotors
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866908307939131392 |
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| author | Li, Guang Chen, Fuxing Fang, Ping |
| author_facet | Li, Guang Chen, Fuxing Fang, Ping |
| contents | 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† 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20071 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | PT -symmetry breaking and universal spectral statistics in quantum kicked rotors Li, Guang Chen, Fuxing Fang, Ping Quantum Physics Statistical Mechanics Chaotic Dynamics Atomic Physics 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† 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. |
| title | PT -symmetry breaking and universal spectral statistics in quantum kicked rotors |
| topic | Quantum Physics Statistical Mechanics Chaotic Dynamics Atomic Physics |
| url | https://arxiv.org/abs/2502.20071 |