Brownian Motion of Charged Particles Driven by Correlated Noise in Magnetic Field

Analytical solutions of the generalized Langevin equation have been found for the time correlation functions describing the motion of a charged Brownian particle in an external magnetic field when the thermal random force in weakly viscoelastic fluids is exponentially correlated in the time. To obtain a correct description at short times, inertial effects are included into the consideration. The found mean square displacement of the particle motion across the field contains a term proportional to the time, a constant term, and exponentially decaying contributions. The solution for a particle trapped in a harmonic well is also found.