Related papers: Potential well in Poincar\'e recurrence
We provide a complete solution of the problems of the probability distribution and the escape rate in Poisson-noise driven systems. It includes both the exponents and the prefactors. The analysis refers to an overdamped particle in a…
A Gedanken experiment is described to explore a counter-intuitive property of quantum mechanics. A particle is placed in a one-dimensional infinite well. The barrier on one side of the well is suddenly removed and the chamber dramatically…
The mechanism of the exponential transient statistics of Poincar\'e recurrences in the presence of chaos border with its critical structure is studied using two simple models: separatrix map and the kicked rotator ('microtron'). For the…
Additive white noise may significantly increase the response of bistable systems to a periodic driving signal. We consider two classes of double-well potentials, symmetric and asymmetric, modulated periodically in time with period $1/\eps$,…
We study the wetting model, which considers a random walk constrained to remain above a hard wall, but with additional pinning potential for each contact with the wall. This model is known to exhibit a wetting phase transition, from a…
When a Brownian particle, initially being in the potential well, overcomes the barrier and moves to the absorptive border, it still has a chance to be scattered back to the well by thermal fluctuations. We study this phenomenon carefully…
In various models and systems involving the escape of periodically forced particle from the potential well, a common pattern is observed. Namely, the minimal forcing amplitude required for the escape exhibits sharp minimum for the…
Suppose we observe a trajectory of length $n$ from an exponentially $\alpha$-mixing stochastic process over a finite but potentially large state space. We consider the problem of estimating the probability mass placed by the stationary…
In this article, we give a semi-analytic expression for survival probability when particles are diffusing in an active potential well. There is no analytic solution available in the literature, due to the requirement of inverse Laplace…
This paper is a first step in the study of the recurrence behavior in random dynamical systems and randomly perturbed dynamical systems. In particular we define a concept of quenched and annealed return times for systems generated by the…
The short time behavior of nucleation probabilities is studied by representing nucleation as diffusion in a potential well with escape over a barrier. If initially all growing nuclei start at the bottom of the well, the first nucleation…
Turbulence has strong and seemingly random fluctuations. Assessing its repeatability is key to predicting flows in technology and nature, much of which decay as viscosity dissipates energy. Much has been done to this end since the work of…
For an ordinary thermodynamical system the Poincar\'{e} recurrence time is exponentially large in the Boltzmann entropy of the system. It turns out, that for a system with dynamical chaos it is determined by the Kolmogorov-Sinai entropy and…
In this numerical study, recurrence quantification analysis of chaotic trajectories is explored to detect atypical dynamical behaviour in non-linear Hamiltonian systems. An ensemble of initial conditions is evolved up to a maximum iteration…
We consider the motion of a damped particle in a potential oscillating slowly between a simple and a double well. The system displays hysteresis effects which can be of periodic or chaotic type. We explain this behaviour by computing an…
The escape rate of a particle over a fluctuating barrier in a double well potential exhibits resonance at an optimum value of correlation time of fluctuation. This has been shown to be important in several variants of kinetic model of…
We compare the classical and quantum mechanical position-space probability densities for a particle in an asymmetric infinite well. In an idealized system with a discontinuous step in the middle of the well, the classical and quantum…
We construct a microscopic model to study discrete randomness in bistable systems coupled to an environment comprising many degrees of freedom. A quartic double well is bilinearly coupled to a finite number $N$ of harmonic oscillators.…
The recurrence phenomena of an initially well localized wave packet are studied in periodically driven power-law potentials. For our general study we divide the potentials in two kinds, namely tightly binding and loosely binding potentials.…
We investigate the escape rate of an overdamped, self-propelled spherical Brownian particle on a surface from a metastable potential well. Within a modeling in terms of a 1D constant speed of the particle's active dynamics we consider the…