Directed momentum current induced by the PT -symmetric driving

Abstract

We investigate the directed momentum current in the quantum kicked rotor model with PT symmetric deriving potential. For the quantum non-resonance case, the values of quasi-energy become to be complex when the strength of imaginary part of the kicking potential exceeds a threshold value, which demonstrates the appearance of the spontaneous PT symmetry breaking. In the vicinity of the transition point, the momentum current exhibits a staircase growth with time. Each platform of the momentum current corresponds to the mean momentum of some eigenstates of the Floquet operator whose imaginary parts of the quasi-energy are significantly large. Above the transition point, the momentum current increases linearly with time. Interestingly, its acceleration rate exhibits a kind of "quantized" increment with the kicking strength. We propose a modified classical acceleration mode of the kicked rotor model to explain such an intriguing phenomenon. Our theoretical prediction is in good agreement with numerical results.

Out-of-time-ordered correlator in non-Hermitian quantum systems

“…It is clear that the quantized increase of G with K is due to the quantized growth of D with K [see Eq. (10)], which has been reported in our previous work [37]. Our theoretical prediction of the quantization of OTOCs is in good agreement with numerical results (see Fig.…”

“…Then, we get the quantized growth of D, i.e., D = 2mπ with K ∈ (2mπ − π, 2mπ + π), which has been numerically verified in Ref. [37].…”

“…where the angular momentum operator p = −i eff ∂/∂θ and θ is the angle coordinate. The parameters eff , K and λ are the effective Planck constant, the strength of the real parts and the imaginary parts of the kicking potential, respectively [37,44,50]. The t n (= 1, 2 .…”

“…As an important modification of quantum mechanics, non-Hermiticity has played versatile roles in describing the open quantum dynamics [32], the non-equilibrium relaxation problems [33], and optical transport in lossy media [34,35]. Novel phenomena induced by non-Hermiticity, for instance, topological insulator [36] and quantized momentum current [37], have garnered research attentions both theoretically [38][39][40] and experimentally [41][42][43]. Previously, we even found that the chaotic dynamics of complex trajectories in non-Hermitian systems can be characterized by the exponential behavior of OTOCs [44].…”

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.…”