Subdiffusion of heavy quark in hot QCD matter by the fractional Langevin equation

TL;DR

This paper models heavy quark subdiffusion in hot QCD matter using the fractional Langevin equation, providing theoretical and numerical insights into their anomalous diffusion behavior and its experimental implications.

Contribution

It introduces a fractional Langevin equation approach with numerical schemes to describe subdiffusive heavy quark dynamics in hot QCD matter, enhancing realism over previous models.

Findings

Heavy quark mean squared displacement deviates from linear time dependence.

Calculated momentum correlation functions and kinetic energy show subdiffusive effects.

Subdiffusion impacts the nuclear modification factor observable in experiments.

Abstract

The subdiffusion phenomena are studied for heavy quarks dynamics in the hot QCD matter. My approach aims to provide a more realistic description of heavy quark dynamics through detailed theoretical analyses and numerical simulations, utilizing the fractional Langevin equation framework with the Caputo fractional derivative. I present numerical schemes for the fractional Langevin equation for subdiffusion and calculate the time evolution mean squared displacement and mean squared momentum of the heavy quarks. My results indicate that the mean squared displacements of the heavy quarks for the subdiffusion process deviate from a linear relationship with time. Further, I calculate the normalized momentum correlation function, kinetic energy, and momentum spread. Finally, I show the effect of subdiffusion on experimental observables, the nuclear modification factor.