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

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† 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.

7 pages with 7 figures

References in corpus (13)

• Making Sense of Non-Hermitian Hamiltonians
• Localization of interacting fermions at high temperature
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• PT-Symmetric Wave Chaos
• Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems
• Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model
• Stationary states of a PT-symmetric two-mode Bose-Einstein condensate
• Realizing PT-symmetric non-Hermiticity with ultra-cold atoms and Hermitian multi-well potentials
• Localization, quantum resonances and ratchet acceleration in a periodically-kicked $\mathcal{P}\mathcal{T}$-symmetric quantum rotator
• Directed momentum current induced by the PT-symmetric driving
• Spacing distribution in the 2D Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at non-integer $\beta$
• Approximation formula for complex spacing ratios in the Ginibre ensemble
• Entropy and entanglement in a bipartite quasi-Hermitian system and its Hermitian counterparts