CENTRA Seminar - Nonlinear dynamics from therelativistic Boltzmann equation in the F-L-R-W spacetime - 2 junho 2016



Nonlinear dynamics from therelativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime

Mauricio Martinez Guerrero

Ohio State University


Abstract / Resumo 

The dissipative dynamics of an expanding massless gas with constant cross section in a spatially flat Friedmann-Lemaı̂tre-Robertson-Walker (FLRW) universe is studied. The mathematical problem of solving the full nonlinear relativistic Boltzmann equation is recast into an infinite set of nonlinear ordinary differential equations for the moments of the one-particle distribution function. Momentum-space resolution is determined by the number of non-hydrodynamic modes included in the moment hierarchy, i.e. by the truncation order. We show that in the FLRW spacetime the non-hydrodynamic modes decouple completely from the slowest hydrodynamic degrees of freedom. This results in the system flowing as an ideal fluid while at the same time producing entropy. The solutions to the nonlinear Boltzmann equation exhibit transient tails of the distribution function with non-trivial momentum dependence. The evolution of this tail is not correctly captured by the relaxation time approximation nor by the linearized Boltzmann equation. However, the latter probes additional high-momentum details unresolved by the relaxation time approximation. While the expansion of the FLRW spacetime is slow enough for the system to move towards (and not away from) local thermal equilibrium, it is not sufficiently slow for the system to actually ever reach complete local equilibrium. Equilibration is fastest in the relaxation time approximation, followed, in turn, by kinetic evolution with a linearized and a fully nonlinear Boltzmann collision term.


2 de junho de 2016 | 14:30

Meeting room on the 2nd floor of the Physics Department building

CENTRA Seminars