Brownian motion and magnetism

TL;DR

This paper explores the relationship between Brownian motion and magnetism, deriving area distributions on a sphere and bounds on free energy for spinless bosons, with implications for polymers, light scattering, and magnetic systems.

Contribution

It introduces a novel connection between Brownian motion and magnetism, providing new analytical tools for understanding magnetic properties and particle entanglement.

Findings

Derived the distribution of areas enclosed by Brownian paths on a sphere

Established a bound on the free energy of spinless bosons in a magnetic field

Linked Brownian motion concepts to magnetic phenomena and polymer entanglement

Abstract

We present an interesting connection between Brownian motion and magnetism. We use this to determine the distribution of areas enclosed by the path of a particle diffusing on a sphere. In addition, we find a bound on the free energy of an arbitrary system of spinless bosons in a magnetic field. The work presented here is expected to shed light on polymer entanglement, depolarized light scattering, and magnetic behavior of spinless bosons.