Ines Aniceto

Analytic approaches to the relativistic Boltzmann equation

The emergence of a universal pre-hydrodynamic attractor behaviour during fluid thermalisation is an important feature in the study of ultra-relativistic nuclear collisions and cold atom experiments. There are several approaches to study this pre-hydrodynamic attractor, one of which is kinetic theory which will be our focus here.

Starting with the relativist Boltzmann equation in the so-called relaxation time approximation, one can introduce a series of moments which solve an infinite cascade of coupled ODEs. We show that these can be written as a single PDE via the introduction of a generating function. We solve this PDE perturbatively for all moments, both in the small and large time approximations, and we then recover the free streaming and attractor regimes at each end via methods of analytic continuation.