  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 the 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 \frac{\hbar}{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.
