Non-extensive Boltzmann Transport Equation: the Relaxation Time Approximation and Beyond

TL;DR

This paper develops approximate analytical solutions to the non-extensive Boltzmann transport equation, compares them with exact solutions, and explores their implications for particle spectra in high-energy collisions and quark-gluon plasma dynamics.

Contribution

It introduces iterative approximate solutions to the non-extensive Boltzmann equation and extends the analysis to non-extensive Fokker-Planck equations for quark-gluon plasma.

Findings

Approximate solutions closely match exact solutions across parameter ranges.

Derived non-extensive Fokker-Planck equation for plasma particle dynamics.

Estimated drag and diffusion coefficients for energetic quarks in gluonic plasma.

Abstract

We derive approximate iterative analytical solutions of the non-extensive Boltzmann transport equation in the relaxation time approximation. The approximate solutions almost overlap with the exact solution for a considerably wide range of the parameter values found in describing particle spectra originated in high-energy collisions. We also discuss the Landau kinetic approximation of the non-extensive Boltzmann transport equation and the emergence of the non-extensive Fokker-Planck equation, and use it to estimate the drag and diffusion coefficients of highly energetic light quarks passing through a gluonic plasma.