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This paper uses dynamical invariants to describe the evolution of collisionless systems subject to time-dependent gravitational forces without resorting to maximum-entropy probabilities. We show that collisionless relaxation can be viewed…
The effects of a "diffusing diffusivity" (DD), a stochastically time-varying diffusion coefficient, are explored within the frameworks of three different forms of fractional Brownian motion (FBM): (i) the Langevin equation driven by…
In the first paper of this series, I investigated whether a wavefunction model of a heavy particle and a collection of light particles might generate "Brownian-Motion-Like" trajectories of the heavy particle. I concluded that it was…
The Brownian motion of a particle in a one-dimensional periodic potential subjected to a uniform external force F is studied. Using the formula for the diffusion coefficient D obtained by other authors and an alternative one derived from…
A Langevin process diffusing in a periodic potential landscape has a time dependent diffusion constant which means that its average mean squared displacement (MSD) only becomes linear at late times. The long time, or effective diffusion…
We analyse the impact of temperature on the diffusion coefficient of an inertial Brownian particle moving in a symmetric periodic potential and driven by a symmetric time-periodic force. Recent studies have revealed the low friction regime…
Transport of point-size Brownian particles under the influence of a constant and uniform force field through a three-dimensional channel with smoothly varying periodic cross-section is investigated. Here, we employ an asymptotic analysis in…
We discuss the dynamics of a Brownian particle under the influence of a spatially periodic noise strength in one dimension using analytical theory and computer simulations. In the absence of a deterministic force, the Langevin equation can…
The bare diffusion coefficient is given as the time integral of the peculiar velocity autocorrelation function or PVACF and this result is different from the well known Green-Kubo formula. The bare diffusion coefficient characterizes the…
Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is $\langle x^2(t)\rangle\simeq\mathscr{K}(t)t$ with…
We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially-dependent diffusion coefficient of the form $D(x)\sim |x|^c$, at constant temperature. The particle's probability distribution function…
We develop the kinetic theory of the flux-carrying Brownian motion recently introduced in the context of open quantum systems. This model constitutes an effective description of two-dimensional dissipative particles violating both…
Many active particles are embedded in environments that exhibit viscoelastic properties. An important class of such media lacks a single characteristic relaxation timescale when subjected to a time-dependent stress. Rather, the stress…
Motivated by subdiffusive motion of bio-molecules observed in living cells we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and…
The one-dimensional overdamped Brownian motion in a symmetric periodic potential modulated by external time-reversible noise is analyzed. The calculation of the effective diffusion coefficient is reduced to the mean first passage time…
Overdamped motion of Brownian particles in tilted piecewise linear periodic potentials is considered. Explicit algebraic expressions for the diffusion coefficient, current, and coherence level of Brownian transport are derived. Their…
Brownian motion is the perpetual irregular motion exhibited by small particles immersed in a fluid. Such random motion of the particles is produced by statistical fluctuations in the collisions they suffer with the molecules of the…
Using simple kinematical arguments, we derive the Fokker-Planck equation for diffusion processes in curved spacetimes. In the case of Brownian motion, it coincides with Eckart's relativistic heat equation (albeit in a simpler form), and…
We present a position Langevin equation for overdamped particle motion on rough two-dimensional surfaces. A Brownian Dynamics algorithm is suggested to evolve this equation numerically, allowing for the prediction of effective (projected)…
We study the asymptotic and pre-asymptotic diffusive properties of Brownian particles in channels whose section varies periodically in space. The effective diffusion coefficient $D_{\mathrm{eff}}$ is numerically determined by the asymptotic…