Non-Markovian thermal-bath-induced Brownian motion in velocity space in the presence of a magnetic field at arbitrary direction

In this work, from the perspective of statistical mechanics, the statistical properties of charged-particle motion in a microwave field and a magnetic field with a general direction described by a generalized Langevin equation subjected to an intrinsic noise with a power-law time decay correlation function have been studied. Using the general expansion theorem for the Laplace transform, the drift velocity of a charged particle in three directions can be expressed in terms of the relaxation functions. Based on the linear response theory, the expression of the complex susceptibilities, the spectral amplification, the stationary form of current density, and the power absorption have been obtained. It is noteworthy that the stochastic dynamics of a charged particle could be induced by fractional Gaussian noise. Additionally, the variances and covariances of charged particles have been studied based on the relations between relaxation functions and memory kernel functions. (paper)