Spectral amplification and power absorption of charged particles under electric field and fluctuating magnetic field

Due to the application of fluctuating magnetic fields in various scientific disciplines, electronic and magnetic transport properties have attracted attention. In this paper, from a statistical mechanics point of view, a Brownian motion model of charged particles characterized by a generalized Langevin equation (GLE) with fluctuating magnetic fields and Ornstein-Uhlenbeck (OU) noise has been studied in detail. The analytic expression for the average particles velocity has been achieved by using the Shapiro-Loginov formular (SLF) and Laplace transform (LT). Furthermore, the exact expressions of the spectral amplification, current density under steady state, as well as relative power absorption have been obtained. Especially, cyclotron resonance, which is relevant in the study of particle physics and physical chemistry, have been further discussed. In addition, the covariance, normalized variance and normalized skewness of charged particle velocity have also been investigated. It is worth pointing out that the fluctuating magnetic field can induce nonlinear resonance behavior of charged particles.