Three transport models for charged particles in three-dimensional semiconductors driven by a fractional noise

In this work, three models of the motion of charged particles in three-dimensional semiconductors governed by a stochastic differential equation driven by a magnetic field and an intrinsic fractional Gaussian noise have been introduced. Based on the general expansion theorem for the Laplace transform, the expressions of the average position and the average velocity of a charged particle have been obtained. The expressions of the complex susceptibilities, the spectral amplification, the stationary form of current density, as well as power absorption also have been obtained. It is worthy to note that the cyclotron resonance, stochastic dynamics of a charged particle could be induced by fractional noise. Furthermore, the expressions of variances and the generalized Fokker–Planck equation (GFPE) for the non-Markovian dynamics also have been investigated.