Equilibration time scales of physically relevant observables

TL;DR

This paper derives a new upper bound on quantum equilibration times for physically relevant observables, providing more realistic estimates especially for systems interacting with thermal baths, advancing understanding of quantum thermalization.

Contribution

It introduces a novel upper bound on equilibration times that is more realistic for physically relevant scenarios, especially in systems coupled to thermal baths.

Findings

New upper bound on equilibration times independent of bath size

Conditions identifying observables with realistic equilibration times

Application to system-bath interactions demonstrating practical relevance

Abstract

We address the problem of understanding from first principles the conditions under which a quantum system equilibrates rapidly with respect to a concrete observable. On the one hand previously known general upper bounds on the time scales of equilibration were unrealistically long, with times scaling linearly with the dimension of the Hilbert space. These bounds proved to be tight, since particular constructions of observables scaling in this way were found. On the other hand, the computed equilibration time scales for certain classes of typical measurements, or under the evolution of typical Hamiltonians, turn out to be unrealistically short. However neither classes of results cover physically relevant situations, which up to now had only been tractable in specific models. In this paper we provide a new upper bound on the equilibration time scales which, under some physically reasonable conditions, give much more realistic results than previously known. In particular, we apply this result to the paradigmatic case of a system interacting with a thermal bath, where we obtain an upper bound for the equilibration time scale independent of the size of the bath. In this way, we find general conditions that single out observables with realistic equilibration times within a physically relevant setup.