Related papers: Regular-to-chaotic tunneling rates using a fictiti…
Filtering is concerned with the sequential estimation of the state, and uncertainties, of a Markovian system, given noisy observations. It is particularly difficult to achieve accurate filtering in complex dynamical systems, such as those…
A standard approach to analyzing tunneling processes in various physical contexts is to use instanton or imaginary time path techniques. For systems in which the tunneling takes place in a time dependent setting, the standard methods are…
Over the preceeding twenty years, the role of underlying classical dynamics in quantum mechanical tunneling has received considerable attention. A number of new tunneling phenomena have been uncovered that have been directly linked to the…
Mode-mode coupling theory is presented for the resonant pumping via dynamical tunneling processes in a deformed microcavity. From the steady-state solution of the coupled differential equations of chaotic modes and a high-Q regular mode,…
Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior…
The occurrence of abrupt dynamical transitions in the macroscopic state of a system has received growing attention. We present experimental evidence for abrupt transition via explosive synchronization in a real-world complex system, namely…
We describe adaptive control algorithms whereby a chaotic dynamical system can be steered to a target state with desired characteristics. A specific implementation considered has the objective of directing the system to a state which is…
This paper deals with the problem of forecast the Logistic Chaotic Map using Fuzzy Times Series (FTS). Chaotic Systems are very sensible to changes in its parameters and in the initial conditions, turning them into hard systems to model 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…
Large deviations in chaotic dynamics have potentially significant and dramatic consequences. We study large deviations of series of finite lengths $N$ generated by chaotic maps. The distributions generally display an exponential decay with…
We describe the statistics of chaotic wavefunctions near periodic orbits using a basis of states which optimise the effect of scarring. These states reflect the underlying structure of stable and unstable manifolds in phase space and…
In this paper we consider the possibility to use numerical simulations for a computer assisted analysis of integrability of dynamical systems. We formulate a rather general method of recovering the obstruction to integrability for the…
We theoretically investigate time-dependent resonant tunneling via two discrete states in an experimentally relevant setup. Our results show that the dc transport through the system can be controled by applying irradiation with a frequency…
We predict that continuously monitored quantum dynamics can be chaotic. The optimal paths between past and future boundary conditions can diverge exponentially in time when there is time-dependent evolution and continuous weak monitoring.…
We consider statistics of electronic transport in chaotic cavities where time-reversal symmetry is broken and one of the leads is weakly non-ideal, i.e. it contains tunnel barriers characterized by tunneling probabilities $\Gamma_i$. Using…
In this paper, we study different types of phase space structures which appear in the context of relativistic chaotic scattering. By using the relativistic version of the H\'{e}non-Heiles Hamiltonian, we numerically study the topology of…
A new type of noised induced phase transitions is proposed. It occurs in noisy systems with dynamical traps. Dynamical traps are regions in the phase space where the regular forces are depressed substantially. By way of an example, a simple…
Chaotic itinerancy is a frequently observed phenomenon in high-dimensional and nonlinear dynamical systems, and it is characterized by the random transitions among multiple quasi-attractors. Several studies have revealed that chaotic…
The dynamics of the kicked-rotor, that is a paradigm for a mixed system, where the motion in some parts of phase space is chaotic and in other parts is regular is studied statistically. The evolution (Frobenius-Perron) operator of phase…
In this paper we develop a perturbation method to predict the rate of occurrence of rare events for singularly perturbed stochastic systems using a probability density function approach. In contrast to a stochastic normal form approach, we…