Once again on molecular Brownian motion and related fundamental 1/f noise: a logical analysis of exact equations

TL;DR

This paper analyzes the exact equations governing a particle in an ideal gas, revealing that they inherently predict significant 1/f-type fluctuations in mobility, which extend to particles in any fluid, shedding light on fundamental noise phenomena.

Contribution

It provides a semi-quantitative analysis of the exact Bogolyubov functional equation, demonstrating its prediction of 1/f noise in particle mobility, a result not previously emphasized.

Findings

Exact equations predict significant 1/f noise in mobility.

The analysis extends the noise prediction to particles in arbitrary fluids.

Comparison with model kinetic equations highlights the importance of exact solutions.

Abstract

The paper contains a simple semi-quantitative analysis of a structure of solution to the exact Bogolyubov functional equation for a particle interacting with ideal gas and driven by an external force, in comparison with solutions to model kinetic equations for the same system. It is shown that the exact equation inevitably predicts existence of significant 1/f-type fluctuations in mobility of the particle, and this result directly extends to particles in arbitrary fluid.