Anomalous diffusion of the heavy quarks through the fractional Langevin equation

The dynamics of heavy quarks within the hot QCD medium have been revisited, considering the influence of anomalous diffusion. This study has been conducted using the framework of the fractional Langevin equation involving the Caputo fractional derivative. We introduce a numerical scheme for the fractional Langevin equation and demonstrate that the mean-squared displacement of the particle exhibits anomalous diffusion, deviating from a linear relationship with time. Our analysis calculates various entities, such as mean-squared momentum, momentum spread, and the nuclear suppression factor <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>R</a:mi><a:mrow><a:mi>A</a:mi><a:mi>A</a:mi></a:mrow></a:msub></a:math>. Notably, our findings indicate that superdiffusion strongly suppresses the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>R</c:mi><c:mrow><c:mi>A</c:mi><c:mi>A</c:mi></c:mrow></c:msub></c:math> compared to normal diffusion in the hot QCD medium. The possible impacts on other parameters are also discussed.