Related papers: Localization for random coupled harmonic oscillato…
We consider a particle in harmonic oscillator potential, whose position is periodically measured with an instrument of finite precision. We show that the distribution of the measured positions tends to a limiting distribution when the…
Macedo and Guedes showed recently how to solve a system of coupled harmonic oscillators with time dependent parameters [{ J. Math. Phys.} {\bf 53}, 052101 (2012)]. We show here that the way in which they get rid of the time dependent masses…
The behaviors of coupled chaotic oscillators before complete synchronization were investigated. We report three phenomena: (1) The emergence of long-time residence of trajectories besides one of the saddle foci; (2) The tendency that orbits…
We investigate the impact of harmonic confinement in a finite optical superlattice and reveal the different mechanisms that can lead to the emergence of localized states. The optical superlattice, with odd or even number of unit cells, can…
We present a theory of Anderson localization on a one-dimensional lattice with translation-invariant hopping. We find by analytical calculation, the localization length for arbitrary finite-range hopping in the single propagating channel…
We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By means of computer simulations we find the relation between the intrinsic dynamics of each member of the population and their mutual interaction that…
By engineering laser-atom interactions, both Hall ribbons and Hall cylinders as fundamental theoretical tools in condensed matter physics have recently been synthesized in laboratories. Here, we show that turning a synthetic Hall ribbon…
We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By studying the intrinsic dynamics of each member of the population and their mutual interactions we observe the emergence of either spatio-temporal…
We study the spatio-temporal behavior of simple coupled map lattices with periodic boundary conditions. The local dynamics is governed by two maps, namely, the sine circle map and the logistic map respectively. It is found that even though…
We study experimentally light localization at phase-slip waveguides and at the intersection of phase-slips in a two-dimensional (2D) square photonic lattice. Such system allows to observe a variety of effects, including the existence of…
We set up and analyze a random matrix model to study energy localization and its time behavior in two chaotically coupled systems. This investigation is prompted by a recent experimental and theoretical study of Weaver and Lobkis on coupled…
We present an approach which enables to identify phase synchronization in coupled chaotic oscillators without having to explicitly measure the phase. We show that if one defines a typical event in one oscillator and then observes another…
We consider a set of N linearly coupled harmonic oscillators and show that the diagonalization of this problem can be put in geometrical terms. The matrix techniques developed here allowed for solutions in both the classical and quantum…
The question under which conditions oscillators with slightly different frequencies synchronize appears in various settings. We show that synchronization can be achieved even for harmonic oscillators that are bilinearly coupled via a purely…
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…
We compare the behaviour of a small truncated coupled map lattice with random inputs at the boundaries with that of a large deterministic lattice essentially at the thermodynamic limit. We find exponential convergence for the probability…
This paper presents the result of the investigation of chaotic oscillator synchronization. A new approach for detecting of synchronized behaviour of chaotic oscillators has been proposed. This approach is based on the analysis of different…
We extend previous work concerning rest-frame partial-wave mixing in Hamiltonian effective field theory to both elongated and moving systems, where two particles are in a periodic elongated cube or have nonzero total momentum, respectively.…
We present an unifying description of a new class of localized states, appearing as large amplitude peaks nucleating over a pattern of lower amplitude. Localized states are pinned over a lattice spontaneously generated by the system itself.…
We analyze the physical mechanisms leading either to synchronization or to the formation of spatio-temporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we…