Non-Markovian stationary probability density for a harmonic oscillator in an electromagnetic field

摘要

We calculate the exact solution of the Fokker-Planck equation for the stationary-state probability density of anharmonic oscillator embedded in an electromagnetic field. The magnetic field is assumed to be a constant andnthe electric field an external stochastic force with the properties of a Gaussian and exponentially correlated noisen(Ornstein-Uhlenbeck process). In this work, we first study the problem in the absence of the magnetic field, thennwe obtain the complete solution and corroborate that the latter reduces to the former when the magnetic field isnsuppressed.