Related papers: Potential well in Poincar\'e recurrence

A discontinuous generalization of the standard map, which arises naturally as the dynamics of a periodically kicked particle in a one dimensional infinite square well potential, is examined. Existence of competing length scales, namely the…

The theory of stochastic resetting asserts that restarting a search process at certain times may accelerate the finding of a target. In the case of a classical diffusing particle trapped in a potential well, stochastic resetting may…

There is a natural connection between two types of recurrence law: hitting times to shrinking targets, and hitting times to a fixed target (usually seen as escape through a hole). We show that for systems which mix exponentially fast, one…

We investigate the short-, medium-, and long-term time dependence of wave packets in the infinite square well. In addition to emphasizing the appearance of wave packet revivals, i.e., situations where a spreading wave packet reforms with…

It is a common phenomenon in nature and technology that a system under perturbations exits a regime of its usual dynamics. Often it is possible to define a potential function whereby a potential well can be associated with a usual or…

We obtain a description of the Poincar\'e recurrences of chaotic systems in terms of the ergodic theory of transient chaos. It is based on the equivalence between the recurrence time distribution and an escape time distribution obtained by…

We investigate the dependence of Poincar\'e recurrence-times statistics on the choice of recurrence-set, by sampling the dynamics of two- and four-dimensional Hamiltonian maps. We derive a method that allows us to visualize the direct…

Starting from a classical mechanics of a ``colloid particle'' and $N$ ``water molecules'', we study effective stochastic dynamics of the particle which jumps between deep potential wells. We prove that the effective transition probability…

In the past few decades considerable effort has been expended in characterizing and modeling financial time series. A number of stylized facts have been identified, and volatility clustering or the tendency toward persistence has emerged as…

A classical scenario for tipping is that a dynamical system experiences a slow parameter drift across a fold tipping point, caused by a run-away positive feedback loop. We study what happens if one turns around after one has crossed the…

We consider the nonequilibrium dynamics of a a real scalar field in a degenerate double-well potential. The system is prepared in the lowest free energy state in one of the wells and the dynamics is driven by the coupling of the field to a…

Escape from a potential well is an extreme example of transient behavior. We consider the escape of the harmonically forced particle under viscous damping from the benchmark truncated weakly nonlinear potential well. Main attention is paid…

The purpose of this paper is to investigate the long time behaviour for a self-interacting diffusion and a self-interacting velocity jump process. While the diffusion case has already been studied for some particular potential function, the…

The quantum form of the Poincar\'e recurrence theorem stipulates that a system with a time-independent Hamiltonian and discrete energy levels returns arbitrarily close to its initial state in a finite time. Qubit systems, being highly…

Under some mild condition, a random walk in the plane is recurrent. In particular each trajectory is dense, and a natural question is how much time one needs to approach a given small neighborhood of the origin. We address this question in…

For a model 1d asymmetric double-well potential we calculated so-called survival probability (i.e. the probability for a particle initially localised in one well to remain there). We use a semiclassical (WKB) solution of Schroedinger…

The paper addresses an escape of a classical particle from a potential well under harmonic forcing. Most dangerous/efficient escape dynamics reveals itself in conditions of 1:1 resonance and can be described in the framework of isolated…

We make a brief review of the Kramers escape rate theory for the probabilistic motion of a particle in a potential well U(x), and under the influence of classical fluctuation forces. The Kramers theory is extended in order to take into…

Systems of particles interacting via inverse-power law potentials have an invariance with respect to changes in length and temperature, implying a correspondence in the dynamics and thermodynamics between different `isomorphic' sets of…

We investigate the statistics of recurrences to finite size intervals for chaotic dynamical systems. We find that the typical distribution presents an exponential decay for almost all recurrence times except for a few short times affected…