Related papers: Delocalization and spreading in a nonlinear Stark …
We develop a formalism relating nonlocal current continuity to spatial symmetries of subparts in discrete Schr\"odinger systems. Breaking of such local symmetries hereby generates sources or sinks for the associated nonlocal currents. The…
Anderson localization is a multiple-scattering phenomenon of linear waves propagating within a disordered medium. Discovered in the late 50s for electrons, it has since been observed experimentally with cold atoms and with classical waves…
The Kronig-Penney model is used to Study the effect of nonlinear interaction on the transmissive properties of both ordered and disordered chains. In the ordered case, the nonlinearity can either localize or delocalize the electronic states…
We study a one-dimensional discrete nonlinear Schr\"odinger model with hopping to the first and a selected N-th neighbor, motivated by a helicoidal arrangement of lattice sites. We provide a detailed analysis of the modulational instability…
Sea ice attenuates waves propagating from the open ocean. Here we model the evolution of energetic unidirectional random waves in the marginal ice zone with a nonlinear Schr\"{o}dinger equation, with a frequency dependent dissipative term…
It is shown that inhomogeneous nonlinear interactions in a Bose-Einstein condensate loaded in an optical lattice can result in delocalizing transition in one dimension, what sharply contrasts to the known behavior of discrete and periodic…
We study numerically propagation of energy in a one dimensional Ding-Ding lattice, composed of linear oscillators with ellastic collisions. Wave propagation is suppressed by breaking translational symmetry, we consider three way to do this:…
In the absence of confinement localization of waves takes place due to randomness or nonlinearity and relies on their phase coherence. We quantitatively probe the sensitivity of localized wave packets to random phase fluctuations and…
We revisit aspects of dynamics and stability of localized states in the deterministic and stochastic discrete nonlinear Schr\"odinger equation. By a combination of analytic and numerical techniques, we show that localized initial conditions…
The existence of localization and mobility edges in one-dimensional lattices is commonly thought to depend on disorder (or quasidisorder). We investigate localization properties of a disorder-free lattice subject to an equally spaced…
We consider nonlinear Schrodinger equations with either local or nonlocal nonlinearities. In addition, we include periodic potentials as used, for example, in matter wave experiments in optical lattices. By considering the corresponding…
In this paper we deal with a nonlinear Schr\"{o}dinger equation with chaotic, random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton evolution, with the strength of the nonlinearity perturbed in the space and time…
We introduce an inhomogeneously-nonlinear Schr{\"o}dinger lattice, featuring a defocusing segment, a focusing segment and a transitional interface between the two. We illustrate that such inhomogeneous settings present vastly different…
It is shown that by properly designing the spatial dependence of the nonlinearity it is possible to induce long-living Bloch oscillations of a localized wavepacket in a periodic potential. The results are supported both by analytical and…
We investigate the dynamics of a single tracer particle performing Brownian motion in a two-dimensional course of randomly distributed hard obstacles. At a certain critical obstacle density, the motion of the tracer becomes anomalous over…
We devise an analytical method to deal with a class of nonlinear Schr\"odinger lattices with random potential and subquadratic power nonlinearity. An iteration algorithm is proposed based on multinomial theorem, using Diophantine equations…
We study the localization aspects of a kicked non-interacting one-dimensional (1D) quantum system subject to either time-periodic or non-periodic pulses. These are reflected as sudden changes of the onsite energies in the lattice with…
Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transitions, the quantum Hall effect, light propagation…
We study the characteristics of chaos evolution of initially localized energy excitations in the one-dimensional nonlinear disordered Klein-Gordon lattice of anharmonic oscillators, by computing the time variation of the fundamental…
A two-dimensional nonlinear Schrodinger lattice with nonlinear coupling, modelling a square array of weakly coupled linear optical waveguides embedded in a nonlinear Kerr material, is studied. We find that despite a vanishing energy…