Stochastic Dynamics in Quenched-in Disorder and Hysteresis

TL;DR

This paper analyzes how quenched-in disorder affects relaxation dynamics and hysteresis, deriving analytical solutions for Wiener-Levy disorder and linking it to the Preisach model.

Contribution

It provides a closed-form analytical solution for hysteresis in systems with Wiener-Levy disorder, connecting stochastic dynamics to the Preisach model.

Findings

Analytical solutions for hysteresis branches with Wiener-Levy disorder

Explicit derivation of Preisach distribution from stochastic dynamics

Demonstration of equivalence between Wiener-Levy disorder and Preisach model

Abstract

The conditions under which relaxation dynamics in the presence of quenched-in disorder lead to rate-independent hysteresis are discussed. The calculation of average hysteresis branches is reduced to the solution of the level-crossing problem for the stochastic field describing quenched-in disorder. Closed analytical solutions are derived for the case where the disorder is characterized by Wiener-Levy statistics. This case is shown to be equivalent to the Preisach model and the associated Preisach distribution is explicitly derived, as a function of the parameters describing the original dynamic problem.