Chaotic dynamics of a non-Hermitian kicked particle

Abstract

We investigate both the classical and quantum dynamics of a kicked particle with P T symmetry. In chaotic situation, the mean energy of the real parts of momentum linearly increases with time, and that of the imaginary momentum exponentially increases. There exists a breakdown time for chaotic diffusion, which is obtained both analytically and numerically. The quantum diffusion of this non-Hermitian system follows the classically chaotic diffusion of Hermitian case during the Ehrenfest time, after which it is completely suppressed. Interestingly, the Ehrenfest time decreases with the decrease of effective Planck constant or the increase of the strength of the non-Hermitian kicking potential. The exponential growth of the quantum out-of-time-order correlators (OTOC) during the initially short time interval characterizes the feature of the exponential diffusion of imaginary trajectories. The long time behavior of OTOC reflects the dynamical localization of quantum diffusion. The dynamical behavior of inverse participation ratio can quantify the P T symmetry breaking, for which the rule of the phase transition points is numerically obtained.

Non-Hermitian Maryland model

“…Contrary to the Hermitian Maryland model, its NH extension shows a richer scenario, with a localization-delocalization phase transition via topological mobility edges in the complex energy plane for irrational α with zero measure L(α) = 0. Our results provide a rather unique example of integrable NH system with aperiodic order, and could have interesting extensions, such as in the study of phase transitions and topological properties of integrable models of two-dimensional NH quasicrystals, and potential relevance in the study of quantum dynamics and quantum chaos in NH Floquet systems [97][98][99][100][101]. Finally, it would be of great interest to consider the NH extension of the Maryland model for irrationals with nonzero measure L(α) > 0 [83], such as Liouvillian numbers, where arithmetic phase transitions [83,95] could compete with NH-driven topological phase transitions.…”

Non-Hermitian Maryland Model

“…Contrary to the Hermitian Maryland model, its non-Hermitian extension shows a richer scenario, with a localization-delocalization phase transition via topological mobility edges in complex energy plane for irrational α with zero measure L(α) = 0. Our results provide a rather unique example of integrable non-Hermitian system with aperiodic order, and could have interesting extensions, such as in the study of phase transitions and topological properties of integrable models of two-dimensional NH quasicrystals, and potential relevance in the study of quantum dynamics and quantum chaos in non-Hermitian Floquet systems [97][98][99][100][101]. Finally, it would be of great interest to consider the NH extension of the Maryland model for irrationals with non-zero measure L(α) > 0 [83], such as Liouvillian numbers, where arithmetic phase transitions [83,94] could compete with non-Hermitian-driven topological phase transitions.…”

Effective protection of quantum coherence by non-Hermitian driving

“…From Fig. 1(a), one can also see that the saturation value of p 2 1 decreases with the increase of λ, which demonstrates that the extent of DL grows as the strength of the non-Hermitian driving increases [48]. To confirm the appearance of DL, we numerically investigate the momentum distribution at the time when the mean value p 2 1 saturates.…”

“…In this letter, we investigate the effects of non-Hermiticity on the quantum coherence, which is displayed by the dynamics of quantum diffusion and entanglement via two coupled kicked rotors with non-Hermitian kicking potential. Interestingly, the results reveal that strong enough non-Hermitian driving can destroy the QCC of the diffusion dynamics and lead to the appearance of DL, which is a signature of the recovery of quantum coherence [48]. The entanglement of the subsystems is gradually reduced by increasing the strength of the non-Hermitian driving, even if the initial state is of maximum entanglement.…”