Thermalization of a strongly interacting closed spin system: From coherent many-body dynamics to a Fokker-Planck equation

TL;DR

This paper derives an analytical Fokker-Planck equation describing thermalization in strongly interacting closed quantum spin systems, revealing how entropy-driven dynamics lead to equilibrium without assuming weak coupling to an environment.

Contribution

The authors analytically connect quantum many-body dynamics to a classical Fokker-Planck equation for the first time in this context, without relying on weak system-bath assumptions.

Findings

Thermalization dynamics are governed by a Fokker-Planck equation.

Transitions within narrow energy shells dominate the relaxation process.

Detailed balance conditions determine the equilibrium state.

Abstract

Thermalization has been shown to occur in a number of closed quantum many-body systems, but the description of the actual thermalization dynamics is prohibitively complex. Here, we present a model - in one and two dimensions - for which we can analytically show that the evolution into thermal equilibrium is governed by a Fokker-Planck equation derived from the underlying quantum dynamics. Our approach does not rely on a formal distinction of weakly coupled bath and system degrees of freedom. The results show that transitions within narrow energy shells lead to a dynamics which is dominated by entropy and establishes detailed balance conditions that determine both the eventual equilibrium state and the non-equilibrium relaxation to it.