  Brownian motion of a heavy charged particle at zero and small (but finite)
temperature is studied in presence of finite density. We are primarily
interested in the dynamics at (near) zero temperature which is holographically
described by motion of a fundamental string in an (near-) extremal
Reissner-Nordstr$\ddot{\text{o}}$m black hole. We analytically compute the
functional form of retarded Green's function for small frequencies and extract
the dissipative behavior at and near zero temperature.
