Quantum Langevin dynamics of a charged particle in a magnetic field: Response function, position–velocity and velocity autocorrelation functions

We use the quantum Langevin equation as a starting point to study response function, position–velocity correlation function and velocity autocorrelation of charged Brownian particle in presence magnetic field linearly coupled heat bath via position coordinate. two models – Ohmic model Drude make detailed comparison various time–temperature regimes. For both models, there is competition between cyclotron frequency viscous damping rate giving rise transition from an oscillatory monotonic behaviour increased. In zero fluctuation dominated low-temperature regime, non-trivial noise correlations lead some interesting features this transition. role memory time-scale which comes into play effect additional time-scale. discuss experimental implications our analysis context experiments cold ions.