Ubiquitous quantum scarring does not prevent ergodicity

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 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. It is generally believed that most eigenstates of quantum chaotic models are ergodic. In this work, the authors disprove this by showing that all eigenstates of the Dicke model in the chaotic regime are scarred, and that ergodicity is an ensemble property, achievable only in the temporal average.

Automated summary

This study reveals that all eigenstates of the chaotic Dicke model are scarred, contradicting the conventional belief that most eigenstates of quantum chaotic models are ergodic. Ergodicity is shown to be an ensemble property, achievable only through temporal averages.