Related papers: Functionals of the Brownian motion, localization a…
Continuous-time random walks offer powerful coarse-grained descriptions of transport processes. We here microscopically derive such a model for a Brownian particle diffusing in a deep periodic potential. We determine both the waiting-time…
Very recent experiments have discovered that localized light in strongly absorbing media displays intriguing diffusive phenomena. Here we develop a first-principles theory of light propagation in open media with arbitrary absorption…
The dynamics of a Brownian particle in a constant magnetic field and time-dependent electric field is studied in the limit of white noise, using a Langevin approach for the classical problem and the path-integral Feynman-Vernon and…
Brownian motion of free particles on curved surfaces is studied by means of the Langevin equation written in Riemann normal coordinates. In the diffusive regime we find the same physical behavior as the one described by the diffusion…
We analyze \emph{fractional Brownian motion} and \emph{scaled Brownian motion} on the two-dimensional sphere $\mathbb{S}^{2}$. We find that the intrinsic long time correlations that characterize fractional Brownian motion collude with the…
We study the Brownian dynamics of a solid particle on a vibrating solid surface. Phenomenologically, the interaction between the two solid surfaces is modeled by solid friction, and the Gaussian white noise models the vibration of the solid…
We analyze the dynamics of Brownian ratchets in a confined environment. The motion of the particles is described by a Fick-Jakobs kinetic equation in which the presence of boundaries is modeled by means of an entropic potential. The cases…
We construct a two-dimensional diffusion process with rank-dependent local drift and dispersion coefficients, and with a full range of patterns of behavior upon collision that range from totally frictionless interaction, to elastic…
We investigate the dynamics of a quantum particle in disordered tight-binding models in one and two dimensions which are exceptions to the common wisdom on Anderson localization, in the sense that the localization length diverges at some…
Transport phenomena are ubiquitous in nature and known to be important for various scientific domains. Examples can be found in physics, electrochemistry, heterogeneous catalysis, physiology, etc. To obtain new information about diffusive…
We study the two-dimensional overdamped motion of an active particle whose orientational dynamics is subject to fractional Brownian noise, whereas its position is affected by self-propulsion and Brownian fluctuations. From a Langevin-like…
We study the diffusion of a Brownian particle quadratically coupled to a thermally fluctuating field. In the weak coupling limit, a path-integral formulation allows to compute the effective diffusion coefficient in the cases of an active…
We analyze the microscopic model of quantum Brownian motion, describing a Brownian particle interacting with a bosonic bath through a coupling which is linear in the creation and annihilation operators of the bath, but may be a nonlinear…
We study the evolution of a collection of individuals subject to Brownian diffusion, reproduction and disappearance. In particular, we focus on the case where the individuals are initially prepared at equilibrium within a confined geometry.…
We revisit the problem of diffusion in a driven system consisting of an inertial Brownian particle moving in a symmetric periodic potential and subjected to a symmetric time-periodic force. We reveal parameter domains in which diffusion is…
We study a simple model for the trajectory of a particle in a turbulent fluid, where a Brownian motion travels through a random Gaussian velocity field. We study the quenched law of the process and prove that in a weak environment setting,…
We derive the joint density of a Skew Brownian motion, its last visit to the origin, local and occupation times. The result is applied to option pricing in a two valued local volatility model and in a displaced diffusion model with…
Consider the first exit time of one-dimensional Brownian motion $\{B_s\}_{s\geq 0}$ from a random passageway. We discuss a Brownian motion with two time-dependent random boundaries in quenched sense. Let $\{W_s\}_{s\geq 0}$ be an other…
We study the Brownian motion of a single particle coupled to an external ac field in a two-dimensional random potential. We find that for small fields a large-scale vorticity pattern of the steady-state net currents emerges, a consequence…
In active Brownian motion, an internal propulsion mechanism interacts with translational and rotational thermal noise and other internal fluctuations to produce directed motion. We derive the distribution of its extreme fluctuations and…