Related papers: Narrow escape of interacting diffusing particles
In this article we address the problem of quantum tunneling of a non-Markovian Brownian particle away from thermal equilibrium. We calculate the Kramers escape rate at low temperature (including the zero temperature case) in the…
We consider Brownian motion in a circular disk $\Omega$, whose boundary $\p\Omega$ is reflecting, except for a small arc, $\p\Omega_a$, which is absorbing. As $\epsilon=|\partial \Omega_a|/|\partial \Omega|$ decreases to zero the mean time…
We present an efficient method to solve the narrow capture and narrow escape problems for the sphere. The narrow capture problem models the equilibrium behavior of a Brownian particle in the exterior of a sphere whose surface is reflective,…
We determine the rate of escape from a potential well, and the diffusion coefficient in a periodic potential, of a random walker that moves under the influence of the potential in between successive collisions with the heat bath. In the…
Nonintersecting motion of Brownian particles in one dimension is studied. The system is constructed as the diffusion scaling limit of Fisher's vicious random walk. N particles start from the origin at time t=0 and then undergo mutually…
We treat the problem of particle pushing by growing ice as a free diffusion near a wall that moves with discrete steps. When the particle diffuse away from the surface the surface can grow, blocking the particle from going back. Elementary…
The escape problem is defined in the context of quantum field theory. The escape rate is explicitly derived for a scalar field governed by fluctuation-dissipation dynamics, through generalizing the standard Kramers problem. In the presence…
Narrow escape and narrow capture problems which describe the average times required to stop the motion of a randomly travelling particle within a domain have applications in various areas of science. While for general domains, it is known…
We investigate a moving boundary problem for a Brownian particle on the semi-infinite line in which the boundary moves by a distance proportional to the time between successive collisions of the particle and the boundary. Phenomenologically…
The condition of thermal equilibrium simplifies the theoretical treatment of fluctuations as found in the celebrated Einstein's relation between mobility and diffusivity for Brownian motion. Several recent theories relax the hypothesis of…
We study the dynamics of one-dimensional active particles confined in a double-well potential, focusing on the escape properties of the system, such as the mean escape time from a well. We first consider a single-particle both in near and…
In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm so-called Walk on Moving Spheres was already introduced in the Brownian context. The aim is…
We discuss escape problem with the consideration of both the activity of particles and the roughness of potentials. we derive analytic expressions for the escape rate of a Brownian particle (ABP) in two types of rough potentials by…
We present a dynamical theory which incorporates the electron-electron correlations and the effects of external magnetic fields for an electron escaping from a helium surface. Analytical expressions for the escape rate can be obtained in…
Many physical processes depend on the time it takes a diffusing particle to find a target. Though this classical quantity is now well-understood in various scenarios, little is known if the diffusivity depends on the location of the…
We introduce and investigate the escape problem for random walkers that may eventually die, decay, bleach, or lose activity during their diffusion towards an escape or reactive region on the boundary of a confining domain. In the case of a…
The diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we…
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…
The physics of activated escape of objects out of a metastable state plays a key role in diverse scientific areas involving chemical kinetics, diffusion and dislocation motion in solids, nucleation, electrical transport, motion of flux…
We discuss the structure and asymptotic long-time properties of coupled equations for the moments of a Brownian particle's momentum derived microscopically beyond the lowest approximation in the weak coupling parameter. Generalized…