Brownian motion of a charged particle driven internally by correlated noise

Abstract

We give an exact solution to the generalized Langevin equation of motion of a charged Brownian particle in a uniform magnetic field that is driven internally by an exponentially correlated stochastic force. A strong dissipation regime is described in which the ensemble-averaged fluctuations of the velocity exhibit transient oscillations that arise from memory effects. Also, we calculate generalized diffusion coefficients describing the transport of these particles and briefly discuss how they are affected by the magnetic field strength and correlation time. Our asymptotic results are extended to the general case of internal driving by correlated Gaussian stochastic forces with finite autocorrelation times.

Effect of Magnetic Field on the Fluctuations of Charged Oscillators in Viscoelastic Fluids

“…These results correct the previous solution [4]. The limits ω → 0 and ω m → ∞ fully correspond to the classical result for particles driven by the white noise in an external magnetic eld [3,8].…”

“…Later Furuse on the basis of the standard Langevin theory with the whitenoise force driving the particles, generalized their results for arbitrary times [3]. The currently observed revival of these problems is mainly related to memory eects in the particle diusion [4,5]. Such eects appear when more realistic coloured random forces act on the particles from their surroundings.…”

Electromagnetic radiation of charged particles in stochastic motion

“…These studies were further extended in [17,18], where it was shown that for a special symmetry of the dynamical friction matrix for Larmor periods of the order of the relaxation time across the magnetic field the diffusion takes place as an ordinary Brownian motion, uninfluenced by the presence of the external magnetic field. The investigation of the Brownian motion of charged particles in stochastic magnetic fields via the use of the Langevin and generalized Langevin equation has become an active field of research with many potential applications in astrophysics, plasma physics, and condensed matter [19][20][21][22][23][24]. The electromagnetic radiation in small-scale random magnetic fields (jitter radiation) and its spectrum, as well as the supplementary acceleration produced by the random variations of the Lorentz force were considered in [25][26][27][28][29][30][31][32][33].…”

Hydrodynamic Memory in the Motion of Charged Brownian Particles across the Magnetic Field

“…Beginning from the works by Taylor [1] and Kurţunođlu [2], the Brownian motion (BM) of charged particles in magnetic fields has been studied in a number of papers (for a review see [3][4][5]). The dynamics of the Brownian particle (BP) was modeled by a Langevin equation (LE) [6] with the Stokes friction and the white--noise stochastic force.…”

“…This results in a generalized LE, which is a Volterra-type integro-differential stochastic equation. For a charged BP in an external magnetic field such equation has been solved in [4] in the case when the memory kernel in the LE exponentially decreases in time. In the present contribution a different kind of memory is considered, the so-called hydrodynamic memory or viscous aftereffect (see [8] and references therein).…”