Non-Markovian Effects on the Brownian Motion of a Free Particle

TL;DR

This paper investigates how non-Markovian effects influence the Brownian motion of a free particle, showing they can increase mean square displacement and momentum, and affect the differentiability of these quantities.

Contribution

It introduces a framework for analyzing non-Markovian effects on Brownian motion using Fokker-Planck equations, highlighting their impact on physical observables.

Findings

Non-Markovian effects enhance mean square displacement.

Non-Markovian effects increase momentum values.

These effects ensure differentiability of observable quantities.

Abstract

Non-Markovian effects upon the Brownian movement of a free particle in the presence as well as in the absence of inertial force are investigated within the framework of Fokker-Planck equations (Rayleigh and Smoluchowski equations). More specifically, it is predicted that non-Markovian features can enhance the values of the mean square displacement and momentum, thereby assuring the mathematical property of differentiability of the these physically observable quantities.