Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa C.P. 09340, CDMX, México.
Phys Rev E. 2019 Dec;100(6-1):062102. doi: 10.1103/PhysRevE.100.062102.
We study the non-Markovian Brownian motion of an electrically charged harmonic oscillator through the action of both a constant magnetic field and time-dependent force fields. The generalized Langevin equation with a friction memory kernel is used to derive the generalized phase-space Fokker-Planck equation for the harmonic oscillator in the absence and in the presence of time-dependent force fields. To achieve our goal, the characteristic function method is applied to obtain, in an accurate way, the theoretical description of the problem. We explicitly calculate the correlation and cross-correlation functions for the position and velocity vectors. We show that the relevant physics behind the theory is contained in the generalized diffusion coefficient, which accounts for the natural coupling between both the harmonic oscillator and magnetic field. Our theoretical results are compared with those previously reported in the literature.
我们通过作用于恒磁场和时变力场来研究电谐振子的非马尔可夫布朗运动。使用带有摩擦记忆核的广义朗之万方程，我们推导出在不存在和存在时变力场情况下谐振子时空间广义福克-普朗克方程。为了达到我们的目标，我们应用特征函数方法，以精确的方式获得问题的理论描述。我们明确地计算了位置和速度矢量的相关和互相关函数。我们表明，理论背后的相关物理量包含在广义扩散系数中，它考虑了谐振子和磁场之间的自然耦合。我们的理论结果与文献中以前报道的结果进行了比较。
