Long-time Tails in Quantum Brownian Motion of a charged particle in a magnetic field

We analyse the long-time tails of a charged quantum Brownian particle in a harmonic potential in the presence of a magnetic field using the Quantum Langevin Equation as a starting point. We analyse the long-time tails in the position-autocorrelation function, position-velocity correlation function and velocity-autocorrelation function. We study these correlations for a Brownian particle coupled to Ohmic and Drude baths, via position coordinate coupling. At finite temperatures we notice a crossover from a power-law to an exponentially decaying behaviour around the thermal time scale ħ k_B/T. We analyse how the appearance of the cyclotron frequency in our study of a charged quantum Brownian particle affects the behaviour of the long time tails and contrast it with the case of a neutral quantum Brownian particle.