Dynamical route to ergodicity and quantum scarring in kicked coupled top

TL;DR

This paper investigates how phase space dynamics influence ergodicity and quantum scarring in a kicked coupled top model, revealing a transition to chaos, deviations from ergodicity, and identifying quantum scars using out-of-time-order correlators.

Contribution

It demonstrates the connection between classical phase space structures and quantum ergodicity and scarring in an interacting spin system, introducing a new method for detecting quantum scars.

Findings

Transition to chaos with increasing kicking strength

Regular islands within chaotic phase space show non-ergodic behavior

Quantum scars linked to unstable orbits and fixed points

Abstract

Unlike classical system, understanding ergodicity from phase space mixing remains unclear for interacting quantum systems due to the absence of phase space trajectories. By considering an interacting spin model known as kicked coupled top, we elucidate the manifestation of phase space dynamics on local ergodic behavior of its quantum counterpart and quantum scarring phenomena. A transition to chaos occurs by increasing the kicking strength, and in the mixed phase space, the islands of regular motions within the chaotic sea clearly exhibit deviation from ergodicity, which we quantify from entanglement entropy and survival probability. Interestingly, the reminiscence of unstable orbits and fixed points can be identified as scars in quantum states, exhibiting athermal behavior and violation of Berry's conjecture for ergodic states. We also discuss the detection of quantum scars by a newly developed method of 'out-of-time-order correlators', which has experimental relevance.