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.

在这项工作中，从统计力学的角度来看，在微波场和磁场中的带电粒子运动的统计特性（由广义Langevin方程描述）受到了幂律时间衰减相关的本征噪声的影响。功能已被研究。使用拉普拉斯变换的一般展开定理，带电粒子在三个方向上的漂移速度可以用弛豫函数表示。基于线性响应理论，获得了复杂磁化率的表示，频谱放大，电流密度的平稳形式以及功率吸收。值得注意的是，带电粒子的随机动力学可能是由分数高斯噪声引起的。此外，