Langevin dynamics and decoherence of heavy quarks at high temperatures

TL;DR

This paper derives a Langevin equation for heavy quarks in high-temperature quark-gluon plasma, analyzing their decoherence and transition from quantum superpositions to classical behavior, with implications for modeling quark dynamics.

Contribution

It introduces a coupled quantum-classical framework for heavy quark dynamics and identifies the decoherence time scale for classical approximation.

Findings

Decoherence time scale $ au o rac{ ext{sqrt}(M)}{ ext{diffusion constant}}$

Heavy quark color state decoheres rapidly at high temperatures

Classical Langevin dynamics are justified after decoherence

Abstract

A Langevin equation of heavy quarks in high-temperature quark-gluon plasma is derived. The dynamics of heavy quark color is coupled with the phase space dynamics and causes a macroscopic superposition state of heavy quark momentum. Decoherence of the superposition state allows one to use a classical description. The time scale of decoherence gives an appropriate discretization time scale $\Delta t\sim \sqrt{M/C_{\rm F}\gamma}$ for the classical Langevin equation, where $M$ is heavy quark mass and $\gamma$ is heavy quark momentum diffusion constant.