Ubiquitous quantum scarring does not prevent ergodicity

TL;DR

This paper demonstrates that in a chaotic quantum system, all eigenstates exhibit scarring along unstable periodic orbits, challenging the assumption that most are ergodic and uniformly distributed in phase space.

Contribution

It reveals that all eigenstates of the chaotic Dicke model are scarred, showing that quantum ergodicity is only an ensemble property after averaging over time.

Findings

All eigenstates are scarred along unstable periodic orbits.

Most states occupy no more than half of the available phase space.

Quantum ergodicity emerges only after temporal averaging.

Abstract

In a classically chaotic system that is ergodic, any trajectory will be arbitrarily close to any point of the available phase space after a long time, filling it uniformly. Using Born's rules to connect quantum states with probabilities, one might then expect that all quantum states in the chaotic regime should be uniformly distributed in phase space. This simplified picture was shaken by the discovery of quantum scarring, where some eigenstates are concentrated along unstable periodic orbits. Despite of that, it is widely accepted that most eigenstates of chaotic models are indeed ergodic. Our results show instead that all eigenstates of the chaotic Dicke model are actually scarred. They also show that even the most random states of this interacting atom-photon system never occupy more than half of the available phase space. Quantum ergodicity is achievable only as an ensemble property, after temporal averages are performed.