Single to Double Hump Transition in the Equilibrium Distribution Function of Relativistic Particles

TL;DR

This paper investigates a transition from single-peaked to bimodal velocity distributions in relativistic fluids as temperature increases, highlighting the effects of relativistic constraints and analyzing various statistical distributions across different dimensions.

Contribution

It reveals a novel velocity distribution transition in relativistic particles and characterizes its nature, including potential experimental observations in two-dimensional systems like graphene.

Findings

Transition from single to bimodal distribution with increasing temperature

Behavior consistent across Bose-Einstein, Fermi-Dirac, and Maxwell-Jüttner distributions

Possible experimental detection in graphene via Johnson-Nyquist noise

Abstract

We unveil a transition from single peaked to bimodal velocity distribution in a relativistic fluid under increasing temperature, in contrast with a non-relativistic gas, where only a monotonic broadening of the bell-shaped distribution is observed. Such transition results from the interplay between the raise in thermal energy and the constraint of maximum velocity imposed by the speed of light. We study the Bose-Einstein, the Fermi-Dirac, and the Maxwell-J\"uttner distributions, all exhibiting the same qualitative behavior. We characterize the nature of the transition in the framework of critical phenomena and show that it is either continuous or discontinuous, depending on the group velocity. We analyze the transition in one, two, and three dimensions, with special emphasis on two-dimensions, for which a possible experiment in graphene, based on the measurement of the Johnson-Nyquist noise, is proposed.