Active velocity processes with suprathermal stationary distributions and long-time tails

TL;DR

This paper presents a unified framework explaining how particles in random force fields with speed-dependent friction develop heavy-tailed velocity distributions and exhibit superdiffusive behavior, relevant for space plasma and driven gases.

Contribution

It introduces a novel model combining active velocity processes with suprathermal stationary distributions and long-time tails, advancing understanding of non-Maxwellian velocity behaviors.

Findings

Heavy tails in velocity distributions emerge under certain conditions.

Long-time velocity autocorrelation indicates persistent high-speed motion.

Superdiffusion of particle position is observed across parameter ranges.

Abstract

When a particle moves through a spatially-random force field, its momentum may change at a rate which grows with its speed. Suppose moreover that a thermal bath provides friction which gets weaker for large speeds, enabling high-energy localization. The result is a unifying framework for the emergence of heavy tails in the velocity distribution, relevant for understanding the power-law decay in the electron velocity distribution of space plasma or more generally for explaining non-Maxwellian behavior of driven gases. We also find long-time tails in the velocity autocorrelation, indicating persistence at large speeds for a wide range of parameters and implying superdiffusion of the position variable.