Nonequilibrium many-body quantum dynamics: from full random matrices to real systems

TL;DR

This paper reviews the study of nonequilibrium quantum dynamics in many-body systems, highlighting how random matrix theory and spectral analysis can predict and interpret complex dynamical behaviors.

Contribution

It demonstrates how features of quantum dynamics can be inferred from spectral properties and how random matrix models support understanding realistic many-body systems.

Findings

Spectral analysis predicts dynamical features like survival probability.

Dynamics can be used to infer spectral properties of the system.

Random matrix theory provides insights into chaotic quantum systems.

Abstract

We present an overview of our studies on the nonequilibrium dynamics of quantum systems that have many interacting particles. Our emphasis is on systems that show strong level repulsion, referred to as chaotic systems. We discuss how full random matrices can guide and support our studies of realistic systems. We show that features of the dynamics can be anticipated from a detailed analysis of the spectrum and the structure of the initial state projected onto the energy eigenbasis. On the other way round, if we only have access to the dynamics, we can use it to infer the properties of the spectrum of the system. Our focus is on the survival probability, but results for other observables, such as the spin density imbalance and Shannon entropy are also mentioned.