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

Area of Science:

• Statistical Physics
• Plasma Physics
• Nonlinear Dynamics

Background:

• Particles in random environments can exhibit complex dynamics.
• Understanding non-Maxwellian velocity distributions is crucial in various physical systems.
• Friction and external forces significantly influence particle behavior.

Purpose of the Study:

• To develop a unifying framework for emergent heavy tails in velocity distributions.
• To explain power-law decay in electron velocity distributions in space plasma.
• To provide a general explanation for non-Maxwellian behavior in driven gases.

Main Methods:

• Analysis of particle dynamics in spatially random force fields.
• Incorporation of speed-dependent friction from a thermal bath.
• Investigation of velocity distributions and velocity autocorrelation functions.

Main Results:

• A framework is established for the emergence of heavy tails in velocity distributions.
• High-energy localization is enabled by friction that weakens at high speeds.
• Long-time tails in velocity autocorrelation indicate persistence at large speeds.
• Superdiffusion of the position variable is implied.

Conclusions:

• The study provides a unified explanation for heavy-tailed velocity distributions.
• The findings are relevant for understanding space plasma and driven gases.
• Persistence at high speeds and superdiffusion are key implications.