Brownian harmonic oscillator driven by white and colored noise in external electric and magnetic fields
The exact and complete descriptions of the motion of a charged Brownian oscillator in crossed external electric and magnetic fields when driven by both white and exponentially-correlated (colored) noise were derived. The 2D diffusion coefficient and mean square displacement (MSD) of the oscillator across the magnetic field were obtained by using the method of velocity autocorrelation functions (VAF) to solve the Langevin equations. In the white noise model, both transport parameters converge to known results when observed in various, such as when there are no external fields present, while in the colored noise model, the transport parameters converge to the white noise limit at long times. Transient oscillations due to the magnetic field are present in both cases, while oscillations due to fluid interaction are observed in the colored noise case.