Related papers: Difference between Devaney chaos associated with t…
We discuss the questions: How to compare quantitatively classical chaos with quantum chaos? Which one is stronger? What are the underlying physical reasons?
The first goal of this note is to prove the strong well-posedness of McKean-Vlasov SDEs driven by L{\'e}vy processes on $\mathbb{R}^d$ having a finite moment of order $\beta \in [1,2]$ and under standard Lipschitz assumptions on the…
We study the occurence of delay mechanisms other than periodic orbits in systems with time dependent potentials that exhibit chaotic scattering. By using as model system two harmonically oscillating disks on a plane, we have found the…
We discuss stochastic resonance-like effects in the context of coupled quantum spin systems. We focus here on an information-theoretic approach and analyze the steady state quantum correlations (entanglement) as well as the global…
A model with hyperchaos is studied by means of Lyapunov two-parameter analysis. The regions of chaos and hyperchaos, as well as autonomous quasiperiodicity are identified. We discuss the picture of domains of different regimes in the…
Classical chaotic systems are distinguished by their sensitive dependence on initial conditions. The absence of this property in quantum systems has lead to a number of proposals for perturbation-based characterizations of quantum chaos,…
This article studies the decoherence induced on a system of two qubits by local interactions with a spin chain with nontrivial internal dynamics (governed by an XY Hamiltonian). Special attention is payed to the transition between two…
We consider environment induced decoherence of quantum superpositions to mixtures in the limit in which that process is much faster than any competing one generated by the Hamiltonian $H_{\rm sys}$ of the isolated system. While the golden…
By using the reduction technique to impulsive differential equations [1], we rigorously prove the presence of chaos in dynamic equations on time scales (DETS). The results of the present study are based on the Li-Yorke definition of chaos.…
We examine the emergence of chaos in a non-linear model derived from a semiquantum Hamiltonian describing the coupling between a classical field and a quantum system. The latter corresponds to a bosonic version of a BCS-like Hamiltonian,…
The Mackey--Glass equation, which was proposed to illustrate nonlinear phenomena in physiological control systems, is a classical example of a simple looking time delay system with very complicated behavior. Here we use a novel approach for…
The intrinsic multivaluedness of interaction process, revealed in Part I of this series of papers, is interpreted as the origin of the true dynamical (in particular, quantum) chaos. The latter is causally deduced as unceasing series of…
This paper studies how complicated and irregular behavior, known as chaos, can arise in a simple mathematical model that includes time delays. The model is a delay differential equation in which the present rate of change depends not only…
Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…
Following a recent work (briefly reviewed below) we consider temporal fluctuations in the reduced density matrix elements for a coupled system involving a pair of kicked rotors as also one made up of a pair of Harper Hamiltonians. These…
Quantum chaos is usually characterized through its statistical implications on the energy spectrum of a given system. In this work we propose a decoherent mechanism for sensing quantum chaos. The chaotic nature of a many-body quantum system…
We study an impact of a random environment on lifetimes of coherent systems with dependent components. There are two combined sources of this dependence. One results from the dependence of the components of the coherent system operating in…
We consider spatiotemporal chaotic systems for which spatial correlation functions decay substantially over a length scale xi (the spatial correlation length) that is small compared to the system size L. Numerical simulations suggest that…
The decay of the overlap between a wave packet evolved with a Hamiltonian H and the same state evolved with H}+$\Sigma $ serves as a measure of the decoherence time $\tau_{\phi}$. Recent experimental and analytical evidence on classically…
High-dimensional chaos displayed by multi-component systems with a single time-delayed feedback is shown to be accessible to time series analysis of a scalar variable only. The mapping of the original dynamics onto scalar time-delay systems…