A Brownian particle having a fluctuating mass

TL;DR

This paper investigates the dynamics of a Brownian particle with fluctuating mass, demonstrating similarities to particles in fluctuating media, validating theoretical predictions through simulations, and exploring implications for non-equilibrium processes.

Contribution

It introduces a model for Brownian particles with fluctuating mass, compares theoretical predictions with simulations, and connects the findings to physical systems involving mass fluctuations.

Findings

Mass velocity distribution matches chi-squared distribution predictions.

Excellent agreement with truncated Tsallis distributions.

Observed interesting behaviors in diffusion and kurtosis over time.

Abstract

We focus on the dynamics of a Brownian particle whose mass fluctuates. First we show that the behaviour is similar to that of a Brownian particle moving in a fluctuating medium, as studied by Beck [Phys. Rev. Lett. 87 (2001) 180601]. By performing numerical simulations of the Langevin equation, we check the theoretical predictions derived in the adiabatic limit, and study deviations outside this limit. We compare the mass velocity distribution with truncated Tsallis distributions [J. Stat. Phys. 52 (1988) 479] and find excellent agreement if the masses are chi- squared distributed. We also consider the diffusion of the Brownian particle by studying a Bernoulli random walk with fluctuating walk length in one dimension. We observe the time dependence of the position distribution kurtosis and find interesting behaviours. We point out a few physical cases where the mass fluctuation problem could be encountered as a first approximation for agglomeration- fracture non equilibrium processes.