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In this paper, we consider the problem of mean first-passage time (MFPT) in quantum mechanics; the MFPT is the average time of the transition from a given initial state, passing through some intermediate states, to a given final state for…
Based on the mean first passage time (MFPT) theory, we derive the expression of the MFPT in the energy-diffusion controlled regime with a power-law distribution. We discuss the finite barrier effect (i.e. thermal energy is not small with…
The stochastic motion of particles in living cells is often spatially inhomogeneous with a higher effective diffusivity in a region close to the cell boundary due to active transport along actin filaments. As a first step to understand the…
The problems of escape from metastable state in randomly flipping potential and of diffusion in fast fluctuating periodic potentials are considered. For the overdamped Brownian particle moving in a piecewise linear dichotomously fluctuating…
The mean first passage time, one of the important characteristics for a stochastic process, is often calculated assuming the observation time is infinite. However, in practice, the observation time, T, is always finite and the mean first…
We study a binary Lennard-Jones system below the glass transition with molecular dynamics simulations. To investigate the dynamics we focus on events ("jumps") where a particle escapes the cage formed by its neighbors. Using single particle…
L\'evy Flights are paradigmatic generalised random walk processes, in which the independent stationary increments---the "jump lengths"---are drawn from an $\alpha$-stable jump length distribution with long-tailed, power-law asymptote. As a…
We consider the mean first passage time of a random walker moving in a potential landscape on a finite interval, starting and end points being at different potentials. From analytical calculations and Monte Carlo simulations we demonstrate…
We investigate the first passage statistics of active continuous time random walks with Poissonian waiting time distribution on a one dimensional infinite lattice and a two dimensional infinite square lattice. We study the small and large…
The transport properties of discrete-time random walks on ring networks with deterministic shortcuts are investigated through analytical and numerical methods. The network consists of a periodic chain where each node is connected to its…
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…
The study of first passage times for diffusing particles reaching target states is foundational in various practical applications, including diffusion-controlled reactions. In this work, we present a bi-scaling theory for the probability…
Biomolecular conformational transitions are usually modeled as barrier crossings in a free energy landscape. The transition paths connect two local free energy minima and transition path times (TPT) are the actual durations of the crossing…
We study the first-passage time (FPT) problem for widespread recurrent processes in confined though large systems and present a comprehensive framework for characterizing the FPT distribution over many time scales. We find that the FPT…
The mean first-passage time (MFPT) is one standard measure for the reaction time in thermally activated barrier-crossing processes. While the relationship between MFPTs and phenomenological rate coefficients is known for systems that…
This paper presents necessary and sufficient conditions for on- and off-diagonal transition probability estimates for random walks on weighted graphs. On the integer lattice and on may fractal type graphs both the volume of a ball and the…
An analytic effective medium theory is constructed to study the mean access times for random walks on hybrid disordered structures formed by embedding complex networks into regular lattices, considering transition rates $F$ that are…
Recent works have explored the properties of L\'evy flights with resetting in one-dimensional domains and have reported the existence of phase transitions in the phase space of parameters which minimizes the Mean First Passage Time (MFPT)…
In this paper we consider three classes of interacting particle systems on $\mathbb Z$: independent random walks, the exclusion process, and the inclusion process. We allow particles to switch their jump rate (the rate identifies the type…
This paper stidies the first passage times to constant boundaries for mixed-exponential jump diffusion processes. Explicit solutions of the Laplace transforms of the distribution of the first passage times, the joint distribution of the…