Transient oscillations in a macroscopic effective theory of the Boltzmann equation

Understand

A new transient effective theory of the relativistic Boltzmann equation is derived for locally momentum-anisotropic systems.

• In the expansion of the distribution function around a local "quasi-equilibrium" state a non-hydrodynamic dynamical degree of freedom is introduced at leading order that breaks local momentum isotropy.
• By replacing the deviation of the distribution function from this quasi-equilibrium state in terms of moments of the leading-order distribution and applying a systematic power counting scheme that orders the non-hydrodynamic modes by their microscopic time scales, a closed set of equations for the dynamical degrees of freedom is obtained.
• Truncating this set at the level of the slowest non-hydroynamic mode we find that it exhibits transient oscillatory behavior -- a phenomenon previously found only in strongly coupled theories, where it appears to be generic.