Glassy Dynamics of Brownian Particles with Velocity-Dependent Friction

TL;DR

This paper investigates a 2D model of Brownian particles with velocity-dependent friction, revealing non-Gaussian velocity distributions, active motion, and broken fluctuation-dissipation relations, using theoretical approaches like Mori-Zwanzig and mode-coupling.

Contribution

It introduces a novel Langevin model with velocity-dependent friction capturing active motion and non-Gaussian velocities, and derives density correlation equations for interacting particles.

Findings

Velocity distribution is non-Gaussian.

Active particles can have negative friction values.

Higher noise strength reduces active particle fraction.

Abstract

We consider a two-dimensional model system of Brownian particles in which slow particles are accelerated while fast particles are damped. The motion of the individual particles are described by a Langevin equation with Rayleigh-Helmholtz velocity dependent friction. In case of noninteracting particles, the time evolution equations lead to a non-Gaussian velocity distribution. The velocity dependent friction allows negative values of the friction or energy intakes by slow particles which we consider as active motion, and also causes breaking of the fluctuation dissipation relation. Defining the effective temperature proportional to the second moment of velocity, it is shown that for a constant effective temperature the higher the noise strength, the lower are the number of active particles in the system. Using the Mori-Zwanzig formalism and the mode-coupling approximation, the equation of motion for the density auto-correlation function are derived. The equations are solved using the equilibrium structure factors. The integration-through-transients approach is used to derive a relation between the structure factor in the stationary state considering the interacting forces, and the conventional equilibrium static structure factor.