Classical Strongly Coupled QGP: VII. Energy Loss

TL;DR

This paper derives the energy loss of a heavy quark in a classical SU(2) Coulomb plasma using linear response theory, revealing strong dependence on coupling strength and agreement with simulations.

Contribution

It provides an analytical expression for heavy quark energy loss in a classical Coulomb plasma valid across all coupling regimes, using the fluctuation-dissipation theorem.

Findings

Energy loss depends strongly on Coulomb coupling b3.

In the liquid phase, energy loss is metallic and soundless.

Analytical results agree with molecular dynamics simulations.

Abstract

We use linear response analysis and the fluctuation-dissipation theorem to derive the energy loss of a heavy quark in the SU(2) classical Coulomb plasma in terms of the $l=1$ monopole and non-static structure factor. The result is valid for all Coulomb couplings $\Gamma=V/K$, the ratio of the mean potential to kinetic energy. We use the Liouville equation in the collisionless limit to assess the SU(2) non-static structure factor. We find the energy loss to be strongly dependent on $\Gamma$. In the liquid phase with $\Gamma\approx 4$, the energy loss is mostly metallic and soundless with neither a Cerenkov nor a Mach cone. Our analytical results compare favorably with the SU(2) molecular dynamics simulations at large momentum and for heavy quark masses.