Self-diffusion constants of non-colliding interacting Brownian motions in one spatial dimension

TL;DR

This paper proves that in one-dimensional systems of interacting Brownian particles, the self-diffusion constants are zero when particles do not collide, using additive functionals of reversible Markov processes.

Contribution

It establishes the vanishing of self-diffusion constants for non-colliding interacting Brownian motions in one dimension, providing a mathematical proof.

Findings

Self-diffusion constants always vanish if particles do not collide.

Representation of self-diffusion constants via additive functionals.

Application of reversible Markov process theory.

Abstract

We prove that self-diffusion constants of interacting Brownian particles in $ \mathbb{R}$ always vanish if the particles do not collide with each other. We represent self-diffusion constants by additive functionals of reversible Markov processes as obtained in O. 1998.