How does relativistic kinetic theory remember about initial conditions?

TL;DR

This paper explores how expanding plasma systems described by the Boltzmann equation in the relaxation time approximation retain information about initial conditions through multiple transient modes with distinct damping and oscillation behaviors.

Contribution

It introduces the concept of infinitely many transient modes in kinetic theory that encode initial conditions, extending the understanding of hydrodynamization beyond holographic models.

Findings

Multiple transient modes carry initial condition information.

Transient modes have exponential damping with power-law and oscillatory features.

Analysis of the interplay between hydrodynamics and transient modes.

Abstract

Understanding hydrodynamization in microscopic models of heavy-ion collisions has been an important topic in current research. Many lessons obtained within the strongly-coupled (holographic) models originate from the properties of transient excitations of equilibrium encapsulated by short-lived quasinormal modes of black holes. This paper aims to develop similar intuition for expanding plasma systems described by a simple model from the weakly-coupled domain, the Boltzmann equation in the relaxation time approximation. We show that in this kinetic theory setup there are infinitely many transient modes carrying information about the initial distribution function. They all have the same exponential damping set by the relaxation time but are distinguished by different power-law suppressions and different frequencies of oscillations, logarithmic in proper time. We also analyze the resurgent interplay between the hydrodynamics and transients in this setup.