Related papers: The narrow escape problem revisited
We extend the work in New J. Phys. 19, 103015 (2017) by deriving a lower bound for the minimum time necessary to implement a unitary transformation on a generic, closed quantum system with an arbitrary number of classical control fields.…
Cell state determination is the outcome of intrinsically stochastic biochemical reactions. Tran- sitions between such states are studied as noise-driven escape problems in the chemical species space. Escape can occur via multiple possible…
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…
Spontaneous persistent motions driven by active processes play a central role to maintain the living cells far from equilibrium. In the majority of the research works, the steady state dynamics of an active system has been described in…
We revise the encounter-based approach to imperfect diffusion-controlled reactions, which employs the statistics of encounters between a diffusing particle and the reactive region to implement surface reactions. We extend this approach to…
The classical theory of chemical reactions can be understood in terms of diffusive barrier crossing, where the rate of a reaction is determined by the inverse of the mean first passage time (FPT) to cross a free energy barrier. Whenever a…
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 study the random walk of a particle in a compartmentalized environment, as realized in biological samples or solid state compounds. Each compartment is characterized by its length $L$ and the boundaries transmittance $T$. We identify two…
We investigate how confinement may drastically change both the probability density of the first-encounter time and the related survival probability in the case of two diffusing particles. To obtain analytical insights into this problem, we…
We study exit times from time-dependent domains under joint perturbations of the trajectory and the domain. Representing a moving domain by a continuous barrier $\Phi$ on space-time, we reduce the exit problem to a one-dimensional…
The first passage search of a diffusing target (prey) by multiple searchers (predators) in confinement is an important problem in the stochastic process literature. While the analogous problem in open space has been studied in some details,…
In this note we discuss limit distribution of normalized return times for shrinking targets and draw a necessary and sufficient condition using sweep-out sequence in order for the limit distribution to be exponential with parameter $1$. The…
Calculating the mean exit time (MET) for models of diffusion is a classical problem in statistical physics, with various applications in biophysics, economics and heat and mass transfer. While many exact results for MET are known for…
Stochastic biochemical and transport processes have various final outcomes, and they can be viewed as dynamic systems with multiple exits. Many current theoretical studies, however, typically consider only a single time scale for each…
The main result in this paper is a variational formula for the exit rate from a bounded domain for a diffusion process in terms of the stationary law of the diffusion constrained to remain in this domain forever. Related results on the…
Diffusion of molecules within biological cells and tissues is strongly influenced by crowding. A key quantity to characterize diffusion is the particle lifetime, which is the time taken for a diffusing particle to exit by hitting an…
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…
This paper considers the narrow escape problem of a Brownian particle within a three-dimensional Riemannian manifold under the influence of the force field. We compute an asymptotic expansion of mean sojourn time for Brownian particles. As…
Activity significantly enhances the escape rate of a Brownian particle over a potential barrier. Whereas constant activity has been extensively studied in the past, little is known about the effect of time-dependent activity on the escape…
We consider processes that coincide with a given diffusion process outside a finite collection of domains. In each of the domains, there is, additionally, a large drift directed towards the interior of the domain. We describe the limiting…