Holographic Brownian motion at finite density

We study holographic Brownian motion of a heavy charged particle at zero and small (but nite) temperature in presence of nite 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 RN black hole. We compute analytically the functional form of retarded Green’s function and also compare that numerically at leading order in small frequency.