Fluctuations from dissipation in a hot non-Abelian plasma

TL;DR

This paper derives spectral functions of microscopic fluctuations in a hot non-Abelian plasma using a classical transport approach, confirming consistency with B"odeker's effective theory and earlier microscopic results.

Contribution

It introduces a Boltzmann-Langevin type transport equation for non-Abelian plasmas to connect fluctuations, dissipation, and entropy, validating B"odeker's effective theory.

Findings

Spectral functions match earlier microscopic results.

B"odeker's effective theory is consistent with fluctuation-dissipation theorem.

Approach applies to ultra-soft modes in hot non-Abelian plasmas.

Abstract

We consider a transport equation of the Boltzmann-Langevin type for non-Abelian plasmas close to equilibrium to derive the spectral functions of the underlying microscopic fluctuations from the entropy. The correlator of the stochastic source is obtained from the dissipative processes in the plasma. This approach, based on classical transport theory, exploits the well-known link between a linearized collision integral, the entropy and the spectral functions. Applied to the ultra-soft modes of a hot non-Abelian (classical or quantum) plasma, the resulting spectral functions agree with earlier findings obtained from the microscopic theory. As a by-product, it follows that B\"odeker's effective theory is consistent with the fluctuation-dissipation theorem.