Persistent many-body quantum echoes

TL;DR

This paper investigates the persistence of quantum many-body echo dynamics under perturbations, revealing that deviations from equilibrium are largely independent of the inversion time, supported by analytical and numerical evidence.

Contribution

It provides a quantitative analytical framework for understanding the robustness of many-body quantum echoes against perturbations, highlighting their persistence over time.

Findings

Deviations are largely independent of the inversion time t ue9.

Analytical predictions match well with numerical simulations.

Quantum echoes show remarkable robustness to perturbations.

Abstract

We consider quantum many-body systems evolving under a time-independent Hamiltonian $H$ from a nonequilibrium initial state at time $t=0$ towards a close-to-equilibrium state at time $t=\tau$. Subsequently, this state is slightly perturbed and finally propagated for another time period $\tau$ under the inverted Hamiltonian $-H$. The entire procedure may also be viewed as an imperfect time inversion or "echo dynamics". We unravel a remarkable persistence of such dynamics with respect to the observable deviations of the time-dependent expectation values from the equilibrium expectation value: For most perturbations, the deviations in the final state are essentially independent of the inversion time point $\tau$. Our quantitative analytical predictions compare very well with exact numerical results.