Can Schrodingerist Wavefunction Physics Explain Brownian Motion? II. The Diffusion Coefficient

TL;DR

This paper explores whether a wavefunction-based model can explain Brownian motion, deriving a criterion for diffusion and an expression for the diffusion coefficient, though exact solutions remain elusive.

Contribution

It introduces a criterion for diffusive motion within wavefunction models and provides an expression for the diffusion coefficient, advancing the understanding of quantum explanations for Brownian motion.

Findings

Diffusive motion can be characterized within wavefunction models.

An explicit expression for the diffusion coefficient is derived.

Exact solutions are not available, limiting direct validation.

Abstract

In the first paper of this series, I investigated whether a wavefunction model of a heavy particle and a collection of light particles might generate "Brownian-Motion-Like" trajectories of the heavy particle. I concluded that it was possible, but left unsettled the second claim in Einstein's classical program: diffusive motion, proportional to the square-root of time, as opposed to ballistic motion, proportional to the time. In this paper, I derive a criterion for diffusive motion, as well as an expression for the diffusion coefficient. Unfortunately, as in paper I, no exact solutions are available for the models, making checking the criterion difficult. But a virtue of the method employed here is that, given adequate information about model eigenvalues and eigenfunctions, diffusion can be definitively ruled in or out.