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We investigate numerically and experimentally the influence of coupling disorder on the self-trapping dynamics in nonlinear one-dimensional optical waveguide arrays. The existence of a lower and upper bound of the effective average…
We have numerically investigated localization properties in the one-dimensional tight-binding model with chaotic binary on-site energy sequences generated by a modified Bernoulli map with the stationary-nonstationary chaotic transition…
We illustrate how dynamical transitions in nonlinear semiclassical models can be recognized as phase transitions in the corresponding -- inherently linear -- quantum model, where, in a Statistical Mechanics framework, the thermodynamic…
We investigate thermalization in a tight-binding chain with an on-site defect subject to local dephasing noise implemented as random phase kicks. For a single linear defect of strength $\epsilon$, we obtain an exact analytical description…
Extensive studies have investigated the transition mechanism of boundary layers initiated by a single primary instability. In a real-world scenario, however, multiple primary instabilities of different physical nature would coexist and…
The nonlinear aspects of longitudinal motion of interacting point masses in a lattice are revisited, with emphasis on the paradigm of charged dust grains in a dusty plasma (DP) crystal. Different types of localized excitations, predicted by…
We consider the spectral and dynamical properties of quantum systems of $n$ particles on the lattice $\Z^d$, of arbitrary dimension, with a Hamiltonian which in addition to the kinetic term includes a random potential with iid values at the…
In the present work we consider a model that has been proposed at the continuum level for self-defocusing nonlinearities in atomic BECs in order to capture phenomenologically the loss of condensate atoms to thermal ones. We explore the…
We present the results of analytical and numerical studies of a one-dimensional nonlocal and nonlinear diffusion equation describing non-equilibrium processes ranging from aggregation phenomena to cooperation of individuals. We study a…
Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional…
The existence and stability of the nonlinear spatial localized modes are investigated in parity-time symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with competing gain and loss profile.…
This work aims to improve generalization and interpretability of dynamical systems by recovering the underlying lower-dimensional latent states and their time evolutions. Previous work on disentangled representation learning within the…
We study a one-dimensional lattice model with site-dependent nearest-neighbor hopping amplitudes that follow a power-law profile. The hopping variation is controlled by a grading exponent, $|alpha|$, which serves as the tuning parameter of…
We study quantum diffusion of wavepackets in one-dimensional random binary subject to an applied electric field. We consider three different cases: Periodic, random, and random dimer (paired) lattices. We analyze the spatial extent of…
This papers presents a formalism describing the dynamics of a quantum particle in a one-dimensional tilted time-dependent lattice. The description uses the Wannier-Stark states, which are localized in each site of the lattice and provides a…
Controlling dopant transport with high spatial precision is crucial for improving the semiconductor functionality, reliability, and scalability. Although prior models of noise-assisted diffusion have been largely confined to idealized one…
We study the Wannier-Stark (WS) localization in one-dimensional amplitude-chirped lattices with the $j$th onsite potential modulated by a function $Fj\cos(2\pi \alpha j)$, where $F$ is the external field with a period determined by…
Light localization by scattering is a fundamental mechanism driving phase transitions of wave transport in disordered systems. Characterizing the localization length in scattering systems is crucial yet challenging. In this Letter, we…
The propagation of stable coherent entities of an electromagnetic field in nonlinear media with parameters varying in space can be described in the framework of iterations of nonlinear integral transformations. It is shown that for a set of…
We analyze and discuss convergence properties of a numerically exact algorithm tailored to study the dynamics of interacting two-dimensional lattice systems. The method is based on the application of the time-dependent variational principle…