Normal mode analysis within relativistic massive transport

TL;DR

This paper analyzes collective modes in relativistic massive particle transport using the linearized Boltzmann equation, revealing mass-dependent behaviors and the impact of Landau damping on dispersion relations.

Contribution

It introduces a normal mode analysis for massive particles, deriving conditions for collective modes and exploring the effects of mass on their properties and damping mechanisms.

Findings

Critical wavenumbers decrease with increasing scaled mass for heat and shear modes.

The sound channel's critical wavenumber varies non-monotonically with mass.

Massive systems exhibit an infinite number of branch points affecting Landau damping.

Abstract

In this paper, we address the normal mode analysis on the linearized Boltzmann equation for massive particles in the relaxation time approximation. One intriguing feature of massive transport is the coupling of the secular equations between the sound and heat channels. This coupling vanishes as the mass approaches zero. By utilizing the argument principle in complex analysis, we determine the existence condition for collective modes and find the onset transition behavior of collective modes previously observed in massless systems. We numerically determine the critical wavenumber for the existence of each mode under various values of the scaled mass. Within the range of scaled masses considered, the critical wavenumbers for the heat and shear channels decrease with increasing scaled mass, while that of the sound channel exhibits a non-monotonic dependence on the scaled mass. In addition, we analytically derive the dispersion relations for these collective modes in the long-wavelength limit. Notably, kinetic theory also incorporates collisionless dissipation effects, known as Landau damping. We find that the branch cut structure responsible for Landau damping differs significantly from the massless case: whereas the massless system features only two branch points, the massive system exhibits an infinite number of such points forming a continuous branch cut.