Ubiquitous quantum scarring does not prevent ergodicity

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 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.

Identification of quantum scars via phase-space localization measures

“…The Dicke model [30] was initially introduced to explain the phenomenon of superradiance [36,43,50,80] and has since fostered a wide variety of theoretical studies, including the behavior of out-of-time-ordered correlators [24,59,63], manifestations of quantum scarring [6,29,35,64,65], non-equilibrium dynamics [1,50,51,57,58,78], and measures of quantum localization with respect to phase space [65,79]. The model is also of great interest to experiments with trapped ions [26,71], superconducting circuits [47], and cavity assisted Raman transitions [5,82].…”

“…Quantum scarring and localization are not synonyms [65], but both carry the idea of confined eigenstates. The notion of localization in quantum systems presupposes a basis representation.…”

“…By comparing the Rényi occupations of the highenergy eigenstates of the Dicke model with the Rényi occupations of random states, as a function of α, we range the eigenstates according to their degree of delocalization. While all eigenstates are scarred [65], the most localized states are the ones scarred by unstable periodic orbits with short periods. The analysis of high-moments (α > 1) of the Husimi functions of these highly localized states allow us to identify more clearly the classical unstable periodic orbits that cause their scarring.…”

How many particles make up a chaotic many-body quantum system?

“…Quantum chaos, especially when caused by particle interactions, has seen a revival in the last decade or so, because it is closely related with topics of high experimental and theoretical in-terest. It is behind the mechanism of thermalization of isolated many-body quantum systems and the validity of the eigenstate thermalization hypothesis (ETH) [1][2][3], it explains the heating of driven systems [4,5], it is the main obstacle for many-body localization [6][7][8][9], it inhibits long-time simulation of many-body quantum systems [10], it can lead to the fast scrambling of quantum information [11], and it is the regime where the phenomenon of quantum scarring may be observed [12][13][14].…”

Quantum-classical correspondence of a system of interacting bosons in a triple-well potential

“…Level statistics as in full random matrices [1], for example, is a quantum signature of classical chaos [2,3]. In the other direction, classical chaos and instability are related with the exponential growth of the out-of-timeordered correlator [4,10], and unstable periodic orbits explain the phenomenon of quantum scarring [11,14]. In this work, we explore the quantum-classical correspondence for yet another goal, that of locating the quantum phase transition points of a system of interacting bosons in a triple-well potential.…”