Abstract
In the present work the generalized Langevin equation is solved for the motion of a charged Brownian oscillator in a magnetic eld, when the thermal random force is exponentially correlated in the time. This model is consistent with the assumption that the medium has weakly viscoelastic properties. The velocity autocorrelation function, time-dependent di usion coe cient and mean square displacement of the particle have been calculated. Our solutions generalize the previous results from the literature and are obtained in a way applicable to other problems of the Brownian motion with memory.
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