Related papers: Escape through a time-dependent hole in the doubli…
We investigate the evolution of families of periodic orbits in a bisymmetrical potential made up of a two-dimensional harmonic oscillator with only one quartic perturbing term, in a number of resonant cases. Our main objective is to compute…
For a class of non-uniformly hyperbolic interval maps, we study rates of escape with respect to conformal measures associated with a family of geometric potentials. We establish the existence of physically relevant conditionally invariant…
We present a novel path-integral method for the determination of time-dependent and time-averaged reaction rates in multidimensional, periodically driven escape problems at weak thermal noise. The so obtained general expressions are…
We investigate dynamics of activated escape in periodically modulated systems. The trajectories followed in escape form diffusion broadened tubes, which are periodically repeated in time. We show that these tubes can be directly observed…
A dynamical theory which incorporates the electron-electron correlations and the effects of external magnetic fields for an electron escaping from a helium surface is presented. The degrees of freedom in the calculation of the escape rate…
If a system mixes too slowly, putting a hole in it can completely destroy the richness of the dynamics. Here we study this instability for a class of intermittent maps with a family of slowly mixing measures. We show that there are three…
We apply periodic orbit theory to study the asymptotic distribution of escape times from an intermittent map. The dynamical zeta function exhibits a branch point which is associated with an asymptotic power law escape. By an analytic…
For a volume preserving map, the exit time, averaged over the incoming set of a region, is given by the ratio of the measure of the accessible subset of the region to that of the incoming set. This result is primarily of interest to show…
We investigate fluid transport in random velocity fields with unsteady drift. First, we propose to quantify fluid transport between flow regimes of different characteristic motion, by escape probability and mean residence time. We then…
The escape rate of a stochastic dynamical system can be found as an expansion in powers of the noise strength. In previous work the coefficients of such an expansion for a one-dimensional map were fitted to a general form containing a few…
In four-dimensional symplectic maps complex instability of periodic orbits is possible, which cannot occur in the two-dimensional case. We investigate the transition from stable to complex unstable dynamics of a fixed point under parameter…
Classical escape in 2D Hamiltonian systems with the mixed state has been studied numerically and analytically. The wide class of potentials with the mixed state is presented by polinomial potentials. In potentials, where the mixed state…
The dynamics of escape from an attractive state due to random perturbations is of central interest to many areas in science. Previous studies of escape in chaotic systems have rather focused on the case of unbounded noise, usually assumed…
We study the escape rate of a particle in a metastable potential in presence of a dissipative bath coupled to the momentum of the particle. Using the semiclassical bounce technique, we find that this rate is exponentially enhanced. In…
Quantum escape of a particle via a time-dependent confining potential in a semi-infinite one-dimensional space is discussed. We describe the time-evolution of escape states in terms of scattering states of the quantum open system, and…
In order to simulate observational and experimental situations, we consider a leak in the phase space of a chaotic dynamical system. We obtain an expression for the escape rate of the survival probability applying the theory of transient…
A comparison of escape rates from one and from two holes in an experimental container (e.g. a laser trap) can be used to obtain information about the dynamics inside the container. If this dynamics is simple enough one can hope to obtain…
Let $T$ be a piecewise expanding interval map and $T_H$ be an abstract perturbation of $T$ into an interval map with a hole. Given a number $\ell$, $0<\ell<1$, we compute an upper-bound on the size of a hole needed for the existence of an…
This paper examines the relationship between the escape rate and the minimal period of the hole. We consider a subshift of finite type on $q$ symbols with a union of $t$ cylinders based at words of identical length $p$ as the hole. The…
Statistical properties for the recurrence of particles in an oval billiard with a hole in the boundary are discussed. The hole is allowed to move in the boundary under two different types of motion: (i) counterclockwise periodic circulation…