Diffusion of Classical Solitons

TL;DR

This paper investigates how classical solitons, such as kinks and skyrmions, diffuse under thermal noise, providing theoretical predictions verified by simulations and revealing entropic forces influencing soliton interactions.

Contribution

It offers a second-order prediction for the diffusion coefficient of kinks in $\

Findings

Predicted kink diffusion coefficient up to second order in temperature.

Numerical simulations confirm theoretical predictions.

Thermal noise induces diffusion and entropic forces among solitons.

Abstract

We study the diffusion and deformation of classical solitons coupled to thermal noise. The diffusion coefficient for kinks in the $\phi^4$ theory is predicted up to the second order in $kT$. The prediction is verified by numerical simulations. Multiskyrmions in the vector O(3) sigma model are studied within the same formalism. Thermal noise results in a diffusion on the multisoliton collective coordinate space (moduli space). There are entropic forces which tend, for example, to bind pairs of solitons into bi-solitonic molecules.