Universality of spectra for interacting quantum chaotic systems

TL;DR

This paper demonstrates that under conditions of strong chaos and decoherence, the spectra of quantum dynamical systems exhibit universal behavior akin to random matrix ensembles, specifically real Ginibre matrices, in large dimensions.

Contribution

It establishes a universal spectral behavior for quantum systems under strong chaos and decoherence, linking their spectra to real Ginibre matrix ensembles in the large dimension limit.

Findings

Spectra have a single eigenvalue at unity, others within a disk in the complex plane.

Radius of the spectral disk depends on the number of measurement operators.

Spectral properties match those of real Ginibre matrix ensembles.

Abstract

We analyze a model quantum dynamical system subjected to periodic interaction with an environment, which can describe quantum measurements. Under the condition of strong classical chaos and strong decoherence due to large coupling with the measurement device, the spectra of the evolution operator exhibit an universal behavior. A generic spectrum consists of a single eigenvalue equal to unity, which corresponds to the invariant state of the system, while all other eigenvalues are contained in a disk in the complex plane. Its radius depends on the number of the Kraus measurement operators, and determines the speed with which an arbitrary initial state converges to the unique invariant state. These spectral properties are characteristic of an ensemble of random quantum maps, which in turn can be described by an ensemble of real random Ginibre matrices. This will be proven in the limit of large dimension.