Anomalous transport of impurities in inelastic Maxwell gases

TL;DR

This paper investigates how impurities in inelastic Maxwell gases exhibit anomalous transport behavior during a non-equilibrium phase transition, revealing potential limitations of hydrodynamic descriptions in such regimes.

Contribution

It introduces a detailed analysis of impurity transport in inelastic Maxwell gases, highlighting a phase transition where traditional hydrodynamics may fail.

Findings

Minority species can carry a finite fraction of total kinetic energy.

The study identifies a non-equilibrium phase transition affecting transport properties.

Behavior of velocity moments is characterized in the ordered phase.

Abstract

A mixture of dissipative hard grains generically exhibits a breakdown of kinetic energy equipartition. The undriven and thus freely cooling binary problem, in the tracer limit where the density of one species becomes minute, may exhibit an extreme form of this breakdown, with the minority species carrying a finite fraction of the total kinetic energy of the system. We investigate the fingerprint of this non-equilibrium phase transition, akin to an ordering process, on transport properties. The analysis, performed by solving the Boltzmann kinetic equation from a combination of analytical and Monte Carlo techniques, hints at the possible failure of hydrodynamics in the ordered region. As a relevant byproduct of the study, the behaviour of the second and fourth-degree velocity moments is also worked out.