On statistics and 1/f noise of molecular random walk in low-density gas

TL;DR

This paper investigates how the statistical properties and 1/f noise in the molecular random walk of a test particle in low-density gas depend on the mass ratio between the particle and gas atoms, using an approximate BBGKY-based model.

Contribution

It introduces a coarsened collisional model that accounts for different masses, revealing the dependence of diffusivity fluctuations on mass ratio and deriving the path distribution.

Findings

Diffusivity fluctuation spectrum exponent varies with mass ratio.

Probability distribution of diffusivity fluctuations is derived.

Path distribution of the test particle is characterized.

Abstract

The random walk of test particle in low-density gas is considered basing on approximate coarsened version of the collisional representation of the BBGKY equations. The coarsening presumes that momentum relaxation rates of the test particle and gas atoms are equal but allows to analyze the case when their masses are different. It is shown that both the spectrum exponent and probability distribution of 1/f-type diffusivity fluctuations of the test particle essentially depend on ratio of the masses, and corresponding distribution of its path is found.