# Nonequilibrium quantum dynamics of many-body systems

## TL;DR

This paper reviews the complex dynamics of one-dimensional spin-1/2 quantum systems, highlighting how initial conditions, Hamiltonian properties, and localization transitions influence their evolution and how spectral information can be inferred from time-dependent data.

## Contribution

It provides a comprehensive overview of nonequilibrium quantum dynamics in many-body systems, emphasizing the role of initial states, Hamiltonian nature, and spectral analysis techniques.

## Key findings

- Different dynamical behaviors at various time scales.
- Correlation hole as a spectral diagnostic tool.
- Insights applicable to cold atom and ion experiments.

## Abstract

We review our results for the dynamics of isolated many-body quantum systems described by one-dimensional spin-1/2 models. We explain how the evolution of these systems depends on the initial state and the strength of the perturbation that takes them out of equilibrium; on the Hamiltonian, whether it is integrable or chaotic; and on the onset of multifractal eigenstates that occurs in the vicinity of the transition to a many-body localized phase. We unveil different behaviors at different time scales. We also discuss how information about the spectrum of a many-body quantum system can be extracted by the sole analysis of its time evolution, giving particular attention to the so-called correlation hole. This approach is useful for experiments that routinely study dynamics, but have limited or no direct access to spectroscopy, as experiments with cold atoms and trapped ions.