Quantum Brownian motion in a magnetic field: Transition from monotonic to oscillatory behaviour

We investigate the Brownian motion of a charged particle in a magnetic field. We study this in the classical and quantum domains. In both domains, we observe a qualitatively interesting transition of the mean square displacement from a monotonic to a damped oscillatory behaviour as one increases the strength of the magnetic field. We notice that these features of the mean square displacement are robust and remain essentially the same for an Ohmic dissipation model and a single relaxation time model for the memory kernel. The predictions stemming from our analysis can be tested against experiments in trapped cold ions.