Test particle description of transport processes for states with a continuous mass spectrum

TL;DR

This paper derives a transport equation for states with a continuous mass spectrum, going beyond quasiparticle approximation, and introduces a test particle method for practical simulations.

Contribution

It presents a novel transport equation that accounts for large state widths and conserved effective particle number, extending beyond quasiparticle models.

Findings

Derived a first-order gradient expansion transport equation.

Identified an exactly conserved effective particle number.

Reformulated the equation into test particle equations of motion.

Abstract

Aiming at a description of transport processes where the dynamically generated width of the states is potentially large a transport equation beyond the quasiparticle approximation is derived in first order gradient expansion. An effective particle number is identified which is exactly conserved by the coarse grained transport equation. Using a test particle ansatz for this conserved quantity allows to rewrite the transport equation into equations of motion for test particles. The two-body collision terms are formulated in terms of the test particles which gain non-trivial renormalization factors due to the coarse graining process.