Related papers: Localization for random coupled harmonic oscillato…
We show that, in the semiclassical limit and whenever the elements of the Hamiltonian matrix are random enough, the eigenvectors of strongly chaotic time-independent systems in ordered bases can on average be exponentially localized across…
In this paper we give a multi-scale analysis proof of \textit{power-law} localization for random operators on ${\Z}^d$ for \textit{arbitrary} $d\geq1$.
We study quantum oscillator lattice systems with disorder, in arbitrary dimension, requiring only partial localization of the associated effective one-particle Hamiltonian. This leads to a many-body localized regime of excited states with…
Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and…
We study under which conditions systems of coupled oscillators on complex networks display remote synchronization, a situation where pairs of vertices, not necessarily physically linked, but with the same network symmetry, are synchronized.
Several theorems are demonstrated that determine the sufficient conditions for the existence of synchronized states (periodical and chaotic) and also of travelling waves in a CML. Also are analytically proven the existence of…
In this paper we study the dynamics of metamaterials composed of high-contrast subwavelength resonators and show the existence of localised modes in such a setting. A crucial assumption in this paper is time-modulated material parameters.…
Synchronization of coupled harmonic oscillators is investigated. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the first and third quadrants) of some projection of the…
We consider an ensemble of globally coupled phase oscillators whose interaction is transmitted at finite speed. This introduces time delays, which make the spatial coordinates relevant in spite of the infinite range of the interaction. We…
We experimentally study the effect of enhancement of localization in weak one-dimensional random potentials. Our experimental setup is a single mode waveguide with 100 tuneable scatterers periodically inserted into the waveguide. By…
We consider a simple two-dimemsional harmonic lattice with random, independent and identically distributed masses. Using the methods of stochastic homogenization, we show that solutions with long wave initial data converge in an appropriate…
Quantum-mechanical observables for spatial and spacetime localization are considered from a lattice-theoretic perspective. It is shown that when replacing the lattice of all complex orthogonal projections underlying the Born rule by the…
We introduce a technique to detect and quantify local functional dependencies between coupled chaotic systems. The method estimates the fraction of locally syncronized configurations, in a pair of signals with an arbitrary state of global…
In this work we investigate the spatiotemporal behaviour of lattices of coupled chaotic logistic maps, where the coupling between sites has a nonlinear form. We show that the stable range of the spatiotemporal fixed point state is…
We consider a random time evolution operator composed of a circuit of random unitaries coupling even and odd neighboring spins on a chain in turn. In spirit of Floquet evolution, the circuit is time-periodic; each timestep is repeated with…
We investigate coupled identical phase oscillators with scale-free distribution of coupling strength. It is shown that partially locked states can occur due to the inhomogeneity in coupling and some properties of the coupling function.…
We study Lyapunov vectors (LVs) corresponding to the largest Lyapunov exponents in systems with spatiotemporal chaos. We focus on characteristic LVs and compare the results with backward LVs obtained via successive Gram-Schmidt…
Photonic lattices have emerged as a promising approach to localize light in space, for example, through topologically protected edge states and Aharonov-Bohm caging. They are of particular importance in the study of flat band systems via…
We study the spectral location of strongly pattern equivariant Hamiltonians arising through configurations on a colored lattice. Roughly speaking, two configurations are "close to each other" if, up to a translation, they "almost coincide"…
The role of restorative coupling on synchronization of coupled identical harmonic oscillators is studied. Necessary and sufficient conditions, under which the individual systems' solutions converge to a common trajectory, are presented.…