Relaxation time approximation with pair production and annihilation processes

TL;DR

This paper extends the Boltzmann equation to include particle transitions in mixtures, deriving hydrodynamic equations and transport coefficients, and clarifies how these coefficients depend on transition times.

Contribution

It introduces a generalized relaxation time approximation for interacting mixtures, establishing constraints and deriving transport coefficients with explicit dependence on transition times.

Findings

Only two independent relaxation time scales are allowed.

Shear and bulk viscosities are independent of transition time.

Bulk viscosity and conductivity of components depend on transition time.

Abstract

We extend the Boltzmann equation in the relaxation time approximation to explicitly include transitions between particles forming an interacting mixture. Using the detailed balance condition as well as conditions of energy-momentum and current conservation, we show that only two independent relaxation time scales are allowed in such an interacting system. Dissipative hydrodynamic equations and the form of transport coefficients is subsequently derived for this case. We find that the shear and bulk viscosity coefficients, as well as the baryon charge conductivity are independent of the transition time scale. However, the bulk viscosity and conductivity coefficients that can be attributed to the individual components of the mixture depend on the transition time.