Related papers: Escapes in Hamiltonian systems with multiple exit …
This paper deals with the derivation and analysis of a seventh-order generalization of the H\'enon-Heiles potential. The new potential has axial and reflection symmetries, and finite escape energy with three channels of escape. Based on…
Driven-dissipative quantum systems can recover stable dynamical attractors in the semiclassical limit, including coexisting limit cycles. At finite fluctuation strength, this classical coexistence becomes quantum metastability: the…
We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…
The physics of activated escape of objects out of a metastable state plays a key role in diverse scientific areas involving chemical kinetics, diffusion and dislocation motion in solids, nucleation, electrical transport, motion of flux…
Transport in Hamiltonian systems with weak chaotic perturbations has been much studied in the past. In this paper, we introduce a new class of problems: transport in Hamiltonian systems with slowly changing phase space structure that are…
Traditionally, Probability theory was dealing with limit theorems where 'limit" means that time tends to infinity. Questions about finite time dynamics (evolution) were always considered as, although important for practical applications,…
Dynamical systems having many coexisting attractors present interesting properties from both fundamental theoretical and modelling points of view. When such dynamics is under bounded random perturbations, the basins of attraction are no…
We present a general mechanism to establish the existence of diffusing orbits in a large class of nearly integrable Hamiltonian systems. Our approach relies on successive applications of the `outer dynamics' along homoclinic orbits to a…
A natural question of how the survival probability depends upon a position of a hole was seemingly never addressed in the theory of open dynamical systems. We found that this dependency could be very essential. The main results are related…
Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed…
We study the noise-induced escape process from chaotic attractors in nonhyperbolic systems. We provide a general mechanism of escape in the low noise limit, employing the theory of large fluctuations. Specifically, this is achieved by…
This paper analyses the Hamiltonian model of drift waves which describes the chaotic transport of particles in the plasma confinement. With one drift wave the system is integrable and it presents stable orbits. When one wave is added the…
This paper studies nonstationary open dynamical systems from the statistical viewpoint. By open, we mean that trajectories may escape through holes in the phase space. By nonstationary, we mean that the dynamical model itself (as well as…
Two generically different but universal dynamical quantum many-body behaviors are discovered by probing the stability of trapped fragmented bosonic systems with strong repulsive finite/long range inter-particle interactions. We use…
We review our results for the dynamics of isolated many-body quantum systems described by one-dimensional spin-1/2 models. We explain how the evolution of these systems depends on the initial state and the strength of the perturbation that…
Invariant manifolds play an important role in organizing global dynamical behaviors. For example, it is found that in multi-well conservative systems where the potential energy wells are connected by index-1 saddles, the motion between…
We consider a stochastic environment with two time scales and outline a general theory that compares two methods to reduce the dimension of the original system. The first method involves the computation of the underlying deterministic…
A continuously measured quantum system with multiple jump channels gives rise to a stochastic process described by random jump times and random emitted symbols, representing each jump channel. While much is known about the waiting time…
The foundations of the chaotic scattering theory for transport and reaction-rate coefficients for classical many-body systems are considered here in some detail. The thermodynamic formalism of Sinai, Bowen, and Ruelle is employed to obtain…
We study deterministic escape dynamics in the framework of the discrete Klein-Gordon modelwith a repulsive quartic on-site potential. Using a combination of analytical techniques, based on differential and algebraic inequalities and…