# Velocity Distribution of Driven Inelastic One-component Maxwell gas

## TL;DR

This paper investigates the velocity distribution in a driven inelastic Maxwell gas, revealing its non-universality and dependence on driving mechanisms, with asymptotic behaviors matching non-interacting models under certain conditions.

## Contribution

It demonstrates that the steady state velocity distribution is non-universal and depends on the driving type, providing insights into the asymptotic behavior matching non-interacting models.

## Key findings

- Velocity distribution depends on the driving mechanism.
- Asymptotic tails match non-interacting models.
- Universal tails occur only with fast-decaying noise.

## Abstract

The nature of the velocity distribution of a driven granular gas, though well studied, is unknown as to whether it is universal or not, and if universal what it is. We determine the tails of the steady state velocity distribution of a driven inelastic Maxwell gas, which is a simple model of a granular gas where the rate of collision between particles is independent of the separation as well as the relative velocity. We show that the steady state velocity distribution is non-universal and depends strongly on the nature of driving. The asymptotic behavior of the velocity distribution are shown to be identical to that of a non-interacting model where the collisions between particles are ignored. For diffusive driving, where collisions with the wall are modelled by an additive noise, the tails of the velocity distribution is universal only if the noise distribution decays faster than exponential.