Memory effect on heavy quarks dynamics in hot QCD matter

The heavy quarks (HQs) are considered to be effective probes to study
the evolution of the QGP. We study the dynamics of HQs in a hot QCD
medium with a time-correlated noise, $\eta$. We have introduced the
effect of memory through $\eta$ and the dissipative force in the
Generalized Langevin equation (GLV). We supposed that the time
correlations of the colored noise decay exponentially with time,
called the memory time, $\tau$. We have explored the effect of
non-zero values of $\tau$ on the nuclear modification factor,
 $R_{AA}$,  and transverse momentum broadening, $\sigma_p$ of the HQs
within the QGP medium. We find that overall memory slows down the
momentum evolution of heavy quarks: in fact, transverse momentum
broadening and the formation of $R_{AA}$are slowed down by memory.
larger.