Onset of Fokker-Planck dynamics within a Closed Finite Spin System

TL;DR

This paper investigates how classical Fokker-Planck relaxation dynamics can emerge within a finite, closed quantum spin system, demonstrating approximate agreement through analytical and numerical methods.

Contribution

It provides the first detailed analysis showing Fokker-Planck type relaxation in a finite quantum system without external baths.

Findings

Magnetization in the spin system relaxes following Fokker-Planck dynamics.

Analytical and numerical results show approximate Fokker-Planck behavior.

Demonstrates emergence of classical-like relaxation in a closed quantum system.

Abstract

Relaxation according to Fokker-Planck equations is a standard scenario in classical statistical mechanics. It is however not obvious how such an equilibration may emerge within a closed, finite quantum system. We present an analytical and numerical analysis of a system comprising sixteen spins in which spatial inhomogeneities of the magnetization relax approximately in accord with a standard Fokker-Planck equation for a Brownian particle in a parabolic potential.