Normal mode analysis within a mutilated relaxation time approximation

TL;DR

This paper analyzes normal modes in kinetic theory using the Boltzmann equation with a mutilated relaxation time approximation, extending hydrodynamic mode analysis to intermediate and short wavelengths and classifying modes as collective or non-collective.

Contribution

It provides a comprehensive order calculation in wavenumber within a modified RTA, including classification of kinetic modes and analysis of hydrodynamic onset transitions.

Findings

Hydrodynamic modes are well separated with energy-independent relaxation time.

Mode classification becomes less clear with energy-dependent relaxation time.

The analysis extends to intermediate and short-wavelength regimes.

Abstract

In this paper, we present a detailed analysis of normal modes based on the Boltzmann equation within the mutilated relaxation time approximation (RTA). Using this linearized effective kinetic description, our analysis encompasses a complete order calculation in wavenumber k, extending the conventional hydrodynamic mode analysis to intermediate and short-wavelength regions. Furthermore, our linear mode analysis can provide a natural classification of kinetic modes into collective modes and non-collective single-particle excitations. In the case of an energy-independent relaxation time, the behavior of hydrodynamic onset transitions is recovered (Romatschke in Eur Phys J C 76:352, 2016). However, for the case with an energy-dependent relaxation time, the distinct classification becomes less clear, as the location of hydrodynamic modes is not well separated from non-hydrodynamic modes.