Anomalous Diffusion in Velocity Space

TL;DR

This paper develops a new theoretical framework for describing anomalous diffusion in velocity space, especially when the probability transition function has a long tail, leading to new equations and coefficients for heavy particles in gases.

Contribution

It introduces a novel general equation for anomalous diffusion in velocity space based on a new approach similar to coordinate space methods.

Findings

Derived a new equation for anomalous diffusion in velocity space.

Calculated effective friction and diffusion coefficients for heavy particles.

Applicable to systems with long-tailed probability transition functions.

Abstract

The problem of anomalous diffusion in the momentum space is considered on the basis of the appropriate probability transition function (PTF). New general equation for description of the diffusion of heavy particles in the gas of the light particles is formulated on basis of the new approach similar to one in coordinate space (S. Trigger et al.). The obtained results permit to describe the various situations when the probability transition function (PTF) has a long tail in the momentum space. The effective friction and diffusion coefficients are found.