Scaling of out-of-time ordered correlators in a non-Hermitian kicked rotor model

TL;DR

This paper explores how out-of-time-ordered correlators behave in a non-Hermitian quantum kicked rotor with PT-symmetry, revealing rapid saturation and size-dependent scaling in the broken PT phase.

Contribution

It introduces a non-Hermitian extension of the quantum kicked rotor model and analyzes the scaling behavior of OTOCs in the PT-symmetry broken phase, combining analytical and numerical methods.

Findings

OTOCs saturate rapidly in the broken PT phase

Late-time saturation value scales as a power-law with system size

Scaling mechanism involves nonlocal operators and time reversal effects

Abstract

We investigate the dynamics of the out-of-time-ordered correlators (OTOCs) via a non-Hermitian extension of the quantum kicked rotor model, where the kicking potential satisfies $\mathcal{PT}$-symmetry. The spontaneous $\cal{PT}$-symmetry breaking emerges when the strength of the imaginary part of the kicking potential exceeds a threshold value. We find, both analytically and numerically, that in the broken phase of $\cal{PT}$ symmetry, the OTOCs rapidly saturate with time evolution. Interestingly, the late-time saturation value scales as a pow-law in the system size. The mechanism of such scaling law results from the interplay between the effects of nonlocal operator in OTOCs and the time reversal induced by non-Hermitian driven potential.