Related papers: Self trapping transition for a nonlinear impurity …
Self-propelled particles accumulate on repulsive barriers in so-called active wetting, but the relationship between this process and equilibrium wetting remains unclear. Using an exact (noiseless) hydrodynamic framework for an active…
We study the dynamics of self-trapping in Bose-Einstein condensates (BECs) loaded in deep optical lattices with Gaussian initial conditions, when the dynamics is well described by the Discrete Nonlinear Schr\"odinger Equation (DNLS). In the…
The longstanding problem of moving discrete solitary waves in nonlinear Schr{\"o}dinger lattices is revisited. The context is photorefractive crystal lattices with saturable nonlinearity whose grand-canonical energy barrier vanishes for…
We investigate the particle trapping and scattering properties in a tight-binding network which consists of several subgraphs. The particle trapping condition is proved under which particles can be trapped in a subgraph without leaking.…
In the quest for signatures of coherent transport we consider exciton trapping in the continuous-time quantum walk framework. The survival probability displays different decay domains, related to distinct regions of the spectrum of the…
We derive threshold equations for self-organization of laser driven atoms in an optical cavity. Our analysis includes probing with either a traveling wave or a retro reflected lattice. These two scenarios lead to qualitatively different…
We study discrete vortices in the anti-continuum limit of the discrete two-dimensional nonlinear Schr{\"o}dinger (NLS) equations. The discrete vortices in the anti-continuum limit represent a finite set of excited nodes on a closed discrete…
The scope of analog simulation in atomic, molecular, and optical systems has expanded greatly over the past decades. Recently, the idea of synthetic dimensions -- in which transport occurs in a space spanned by internal or motional states…
A dynamic symmetry-breaking transition with noise and inertia is analyzed. Exact solution of the linearized equation that describes the critical region allows precise calculation (exponent and prefactor) of the number of defects produced as…
This paper deals with transient stability in interconnected micro-grids. The main contribution involves i) robust classification of transient dynamics for different intervals of the micro-grid parameters (synchronization, inertia, and…
We study the formation of stationary localized states using the discrete nonlinear Schr\"{o}dinger equation in a Cayley tree with connectivity $K$. Two cases, namely, a dimeric power law nonlinear impurity and a fully nonlinear system are…
The connection between symmetries and conservation laws is a cornerstone of physics. It underlies Bloch's theorem which explains wave phenomena in all linear periodic systems. Here we demonstrate that, in a nonlinear grating with memory,…
We discuss the existence of breathers and lower bounds on their power, in nonlinear Schr\"odinger lattices with nonlinear hopping. Our methods extend from a simple variational approach to fixed point arguments, deriving lower bounds for the…
We report the first observation of robust self-trapping of vortex beams propagating in a uniform condensed medium featuring local saturable self-focusing nonlinearity. Optical vortices with topological charge m=1, that remain self-trapped…
We examine a fractional version of the discrete Nonlinear Schr\"{o}dinger (dnls) equation, where the usual discrete laplacian is replaced by a fractional discrete laplacian. This leads to the replacement of the usual nearest-neighbor…
Localization-delocalization transition in a discrete Anderson nonlinear Schr\"odinger equation with disorder is shown to be a critical phenomenon $-$ similar to a percolation transition on a disordered lattice, with the nonlinearity…
We theoretically and experimentally examine the effect of forcing and damping on systems that can be described by the nonlinear Schr\"odinger equation (NLSE), by making use of the phase-space predictions of the three-wave truncation of the…
The deconfinement transition is studied close to the continuum limit of SO(3) lattice gauge theory. High barriers for tunnelling among different twist sectors causing loss of ergodicity for local update algorithms are circumvented by means…
Schr\"odinger equations with nonlinearities concentrated in some regions of space are good models of various physical situations and have interesting mathematical properties. We show that in the semiclassical limit it is possible to…
The paper is focused on the dynamic homogenization of lattice-like materials with lumped mass at the nodes to obtain energetically consistent models providing accurate descriptions of the acoustic behavior of the discrete system. The…