Dynamics of measured many-body quantum chaotic systems

TL;DR

This paper investigates the dynamics of many-body chaotic quantum systems under continuous measurement, analyzing state purification and phase stability through analytical and numerical methods, including an effective replica theory.

Contribution

It introduces an analytical framework for understanding measurement effects in many-body quantum chaos, including an effective replica theory for phase stability.

Findings

Strong and weak measurement regimes characterized analytically.

Monitoring times can be exponentially long in particle number.

Numerical simulations confirm analytical predictions.

Abstract

We consider the dynamics of continuously measured many-body chaotic quantum systems. Focusing on the observable of state purification, we analytically describe the limits of strong and weak measurement rate, where in the latter case monitoring up to time scales exponentially long in the numbers of particles is required. We complement the analysis of the limiting regimes with the construction of an effective replica theory providing information on the stability and the symmetries of the respective phases. The analytical results are tested by comparison to exact numerical simulations for a measured SYK model.