Stable Energy Distribution of Weakly Dissipative Gasses under Collisional Energy Cascades

TL;DR

This paper demonstrates that the steady-state energy distribution in weakly dissipative gases undergoing collisional energy cascades can be accurately described by a generalized Mittag-Leffler distribution, revealing universal behavior across different systems.

Contribution

It introduces a universal analytical form for the steady-state energy distribution in dissipative gases, connecting it to stable distributions and validating it through simulations and experiments.

Findings

The energy distribution follows a generalized Mittag-Leffler form.

The distribution exhibits a power-law tail similar to Levy stable distributions.

Universality is confirmed across simulations and plasma experiments.

Abstract

Collisional thermalization of a particle ensemble under the energy dissipation can be seen in variety of systems, such as heated granular gasses and particles in plasmas. Despite its universal existence, analytical descriptions of the steady-state distribution have been missing. Here, we show that the steady-state energy distribution of the wide class of collisional energy cascades can be well approximated by the generalized Mittag-Leffler distribution, which is one of stable distributions. This distribution has a power-law tail, as similar to Levy's stable distribution, the index of which is related to the energy dissipation rate. We demonstrate its universality by comparing Mont-Carlo simulations of dissipative gasses as well as the spectroscopic observation of the atom velocity distribution in a low-temperature plasma.