Compelling Bounds on Equilibration Times -- the Issue with Fermi's Golden Rule

TL;DR

This paper critically examines the applicability of a proposed universal bound on equilibration times in closed quantum systems, revealing limitations of Fermi's Golden Rule through numerical analysis of finite spin systems.

Contribution

It demonstrates the breakdown of Fermi's Golden Rule in finite-sized systems, challenging the assumptions behind recent bounds on quantum equilibration times.

Findings

Fermi's Golden Rule fails in superweak coupling regimes for finite baths.

Standard quantum master equations break down in certain parameter regimes.

Numerical simulations of spin systems illustrate these limitations.

Abstract

Putting a general, physically relevant upper bound on equilibration times in closed quantum systems is a recently much pursued endeavor. In PRX, 7, 031027 (2017) Garc\'{\i}a-Pintos et al. suggest such a bound. We point out that the general assumptions which allow for an actual estimation of this bound are violated in cases in which Fermi's Golden Rule and related open quantum system theories apply. To probe the range of applicability of Fermi's Golden Rule for systems of the type addressed in the above work, we numerically solve the corresponding Schr\"odinger equation for some finite spin systems comprising up to 25 spins. These calculations shed light on the breakdown of standard quantum master equations in the "superweak" coupling limit, which occurs for finite sized baths.