Bounds in Nonequilibrium Quantum Dynamics

TL;DR

This paper reviews recent theoretical bounds on out-of-equilibrium quantum dynamics, including speed limits, equilibration, locality constraints, entanglement growth, and error bounds, providing a comprehensive overview for researchers.

Contribution

It offers a systematic review of various bounds in nonequilibrium quantum dynamics, highlighting recent progress and unifying different aspects of the field.

Findings

Summarizes universal speed limits for quantum and classical systems.

Reviews bounds on quantum thermalization and equilibration.

Discusses Lieb-Robinson bounds and entanglement dynamics.

Abstract

We review various bounds concerning out-of-equilibrium dynamics in few-level and many-body quantum systems. We primarily focus on closed quantum systems but will also mention some related results for open quantum systems and classical stochastic systems. We start from the speed limits, the universal bounds on the speeds of (either quantum or classical) dynamical evolutions. We then turn to review the bounds that address how good and how long would a quantum system equilibrate or thermalize. Afterward, we focus on the stringent constraint set by locality in many-body systems, rigorously formalized as the Lieb-Robinson bound. We also review the bounds related to the dynamics of entanglement, a genuine quantum property. Apart from some other miscellaneous topics, several notable error bounds for approximated quantum dynamics are discussed. While far from comprehensive, this topical review covers a considerable amount of recent progress and thus could hopefully serve as a convenient starting point and up-to-date guidance for interested readers.