Related papers: Localized states in bistable pattern forming syste…
We study localized modes on a single Ablowitz-Ladik impurity embedded in the bulk or at the surface of a one-dimensional linear lattice. Exact expressions are obtained for the bound state profile and energy. Dynamical excitation of the…
We study the spatial structure of wave functions with exceptionally high local amplitudes in the Anderson model of localisation. By means of exact diagonalisations of finite systems, we obtain and analyse images of these wave functions: we…
In disordered systems, the amplitudes of the localized states will decrease exponentially away from their centers and the localization lengths are characterizing such decreasing. In this article, we find a model in which each eigenstate is…
We study the existence of one-dimensional localized states supported by linear periodic potentials and a domain-wall-like Kerr nonlinearity. The model gives rise to several new types of asymmetric localized states, including single- and…
We propose a simplified version of the Multi-Scale Analysis of tight-binding Anderson models with strongly mixing random potentials which leads directly to uniform exponential bounds on decay of eigenfunctions in arbitrarily large finite…
Optical localized states are usually defined as self-localized bistable packets of light which exist as independently controllable optical intensity pulses either in the longitudinal or transverse dimension of nonlinear optical systems.…
We study the localization phenomena in a one-dimensional lattice system with a uniformly moving disordered potential. At a low moving velocity, we find a sliding localized phase in which the initially localized matter wave adiabatically…
We study the linear stability properties of spatially localized single- and multi-peak states generated in a subcritical Turing bifurcation in the Meinhardt model of branching. In one spatial dimension, these states are organized in a…
We study self-trapped localized nonlinear states in the form of truncated Bloch waves in one-dimensional optical lattices, which appear in the gaps of the linear bandgap spectrum. We demonstrate the existence of families of such localized…
Systems with quasiperiodic disorder are known to exhibit localization transition in low dimension. After a critical strength of disorder all the states of the system become localized, thereby ceasing the particle motion in the system.…
In this article, we analyze a nonlocal ring network of adaptively coupled phase oscillators. We observe a variety of frequency-synchronized states such as phase-locked, multicluster and solitary states. For an important subclass of the…
We study the influence of a linear nonlocal spatial coupling on the interaction of fronts connecting two equivalent stable states in the prototypical 1-D real Ginzburg-Landau equation. While for local coupling the fronts are always…
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 analyze the formation of localized structures in cavity-enhanced second-harmonic generation. We focus on the phase-matched limit, and consider that fundamental and generated waves have opposite sign of group velocity dispersion. We show…
We investigate the processes of synchronization and phase ordering in a system of globally coupled maps possessing bistable, chaotic local dynamics. The stability boundaries of the synchronized states are determined on the space of…
Photonic topological structures supporting spin-momentum locked topological states underpin a plethora of prospects and applications for disorder-robust routing of light. One of the cornerstone ideas to realize such states is to exploit…
We demonstrate emergence of a complex state in a homogeneous ensemble of globally coupled identical oscillators, reminiscent of chimera states in locally coupled oscillator lattices. In this regime some part of the ensemble forms a…
We report about a mechanism for surface localization, present in finite defect-free polyatomic lattices described by a tight binding model. Numerical diagonalization and degenerated perturbation theory show that there is a minimum number of…
Strongly interacting systems are characterized by heavily dressed entities with internal degrees of freedom, which, on a local level, can be described in terms of coherent quantum states. We examine the modification of these local coherent…
We investigate how imposing kinetic restrictions on quantum particles that would otherwise hop freely on a two-dimensional lattice can lead to topologically ordered states. The kinetically constrained models introduced here are derived as a…