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 nonhydrodynamic 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 nonhydrodynamic 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 nonhydroynamic mode, we find that it exhibits transient oscillatory behavior—a phenomenon previously found only in strongly coupled theories, where it appears to be generic. In weakly coupled systems described by the Boltzmann equation, these transient oscillations depend on the breaking of local momentum isotropy being treated nonperturbatively at leading order in the expansion of the distribution function.

• Received 23 July 2015

DOI:https://doi.org/10.1103/PhysRevD.93.034002