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 harmonic potential presence magnetic field using Quantum Langevin Equation as starting point. position-autocorrelation function, position–velocity correlation function and velocity-autocorrelation function. study these correlations for coupled to Ohmic Drude baths, via position coordinate coupling. At finite temperatures we notice crossover from power-law an exponentially decaying behaviour around thermal time scale ħkBT. how appearance cyclotron frequency our affects long contrast it with case neutral particle.