Dissipation and decoherence for generic open quantum systems

TL;DR

This paper investigates the spectral properties, dissipative regimes, and quantum chaos signatures of generic open quantum systems with Markovian dissipation, combining numerical analysis and analytical formulas to understand their long-term dynamics.

Contribution

It provides a comprehensive numerical and analytical study of spectral features, dissipation regimes, and chaos indicators in generic open quantum systems with random dissipation channels.

Findings

Identification of three dissipation regimes with distinct scaling behaviors.

Analytical expressions for spectral gap at arbitrary dissipation strength.

Discovery of a complex spacing ratio as a signature of quantum chaos.

Abstract

We study generic open quantum systems with Markovian dissipation, focusing on a class of stochastic Liouvillian operators of Lindblad form with independent random dissipation channels (jump operators) and a random Hamiltonian. We perform a thorough numerical study, focusing on global spectral features, the spectral gap, and the steady-state purity and statistics. We establish that all properties follow three different regimes as a function of the dissipation strength, whose boundaries depend on the particular observable. Within each regime, we determine the scaling exponents with the dissipation strength and system size. On the analytical side, we compute the average spectral gap at arbitrary dissipation and provide simple closed-form expressions for the asymptotic values at strong and weak dissipation strength. We also consider spectral correlations in generic complex spectra, such as that of the Liouvillian. We introduce and study, both analytically and numerically, the complex ratio of the nearest-neighbor spacing by next-to-nearest-neighbor spacing. Besides the usual level repulsion, we find that complex spacing ratios have a nontrivial angular dependence which offers a distinct signature of quantum chaos. It distinguishes integrable systems, which support the flat ratio distribution characteristic of Poisson statistics, and chaotic dissipative quantum systems, which conform to Random Matrix Theory statistics. We apply this new signature of quantum chaos to random Liouvillians and boundary-driven dissipative spin-chains. The results of this thesis can help understand the long-time dynamics, steady-state properties, and spectral correlations of generic dissipative systems.