Abstract
In this paper, we study the basic problem of a charged particle in a stochastic magnetic field. We consider dichotomous fluctuations of the magnetic field where the sojourn time in one of the two states are distributed according to a given waiting-time distribution either with Poisson or non-Poisson statistics, including as well the case of distributions with diverging mean time between changes of the field, corresponding to an ergodicity breaking condition. We provide analytical and numerical results for all cases evaluating the average and the second moment of the position and velocity of the particle. We show that the field fluctuations induce diffusion of the charge with either normal or anomalous properties, depending on the statistics of the fluctuations, with distinct regimes from those observed, e.g., in standard Continuous-Time Random Walk models.
Highlights
Diffusive processes occur in many physical, chemical and engineering applications.When the diffusion process is taking place, the quantities related to the spreading species take random values
We have introduced a complete framework to describe the motion of a charged particle in a fluctuating magnetic field
We find that in the case of ergodic fluctuations the diffusion is asymptotically normal, while for non-ergodic fluctuations, we find anomalous diffusion properties
Summary
Diffusive processes occur in many physical, chemical and engineering applications.When the diffusion process is taking place, the quantities related to the spreading species take random values. Diffusive processes occur in many physical, chemical and engineering applications. Since Einstein and Smoluchowski’s work on Brownian motion [1,2], diffusive phenomena have been a fundamental subject of intense research. Both derivations (Einstein and Smoluchowski’s) lead to the well-known diffusion relationship, in the onedimensional case, h x2 i = 2Dt, with D the diffusion coefficient. Several relevant physical and biological phenomena have been discovered in the last few decades, showing an anomalous relationship between mean-squared displacement and time, h x2 i ∝ tα. Diffusion through porous media or within a crowded cellular environment, making anomalous diffusion a relevant subject of research work [3,4,5,6] and Refs. Diffusion through porous media or within a crowded cellular environment, making anomalous diffusion a relevant subject of research work [3,4,5,6] and Refs. [7,8] for a review
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