Probing the hue of the stochastic magnetization dynamics

TL;DR

This paper explores the dynamics of stochastic magnetization by mapping the Fokker-Planck equation to a Schrödinger equation, providing new insights into the evolution of probability distributions in magnetic systems.

Contribution

It introduces a novel approach of mapping the Fokker-Planck equation to a Schrödinger equation to analyze magnetization dynamics.

Findings

Mapping reveals new analytical solutions

Provides a deeper understanding of equilibration times

Connects stochastic magnetization to quantum analogs

Abstract

The Fokker--Planck equation describes the evolution of a probability distribution towards equilibrium--the flow parameter is the equilibration time. Assuming the distribution remains normalizable for all times, it is equivalent to an open hierarchy of equations for the moments. Ways of closing this hierarchy have been proposed; ways of explicitly solving the hierarchy equations have received much less attention. In this paper we show that much insight can be gained by mapping the Fokker--Planck equation to a Schr\"odinger equation, where Planck's constant is identified with the diffusion coefficient.