Divergence and resummation of the moment expansion for an ultrarelativistic gas in Bjorken flow

TL;DR

This paper reveals the divergence of the moment expansion for an ultrarelativistic gas in Bjorken flow, applies Borel-Padé resummation to recover the distribution function, and compares it with Boltzmann solutions to study deviations from equilibrium.

Contribution

It is the first to demonstrate divergence in the moment expansion and to apply Borel-Padé resummation for this system, providing new insights into non-equilibrium behavior.

Findings

Moment expansion diverges for ultrarelativistic Bjorken flow

Borel-Padé resummation successfully reconstructs the distribution function

Significant deviations from local equilibrium observed

Abstract

In this letter, we demonstrate for the first time that the moment expansion for an ultrarelativistic gas undergoing Bjorken flow diverges. We then show how this series can be resummed using the Borel-Pad\'e method and use this to determine the single-particle distribution function of the gas. Finally, we compare the exact resummed solution of the single-particle distribution function with solutions of the Boltzmann equation in the hydrodynamic limit and verify that the system displays considerable deviations from local equilibrium.