Angular mode expansion of the Boltzmann equation in the small-angle approximation

Understand

We use an expansion in angular mode functions in order to solve the Boltzmann equation for a gluon plasma undergoing longitudinal expansion.

• By comparing with the exact solution obtained numerically by other means we show that the expansion in mode functions converges rapidly for all cases of practical interest, and represents a substantial gain in numerical effort as compared to more standard methods.
• We contrast the cases of a non expanding plasma and of longitudinally expanding plasmas, and follow in both cases the evolutions towards thermalization.
• In the latter case, we observe that, although the spherical mode function appears to be well reproduced after some time by a local equilibrium distribution function depending on slowly varying temperature and chemical potential, thereby suggesting thermalization of the system, the longitudinal and transverse pressures take more time to equilibrate.