Related papers: Nonlinear Anderson localization in Toda lattices
We study Anderson localization in quasi--one--dimensional disordered wires within the framework of the replica $\sigma$--model. Applying a semiclassical approach (geodesic action plus Gaussian fluctuations) recently introduced within the…
One of the daunting challenges in optical physics is to accurately control the flow of light at the subwavelength scale, by patterning the optical medium one can design anisotropic media. The light transport can also be significantly…
Wave localization is ubiquitous in disordered media -- from amorphous materials, where soft-mode localization is closely related to materials failure, to semi-conductors, where Anderson localization leads to metal-insulator transition. Our…
It is classical, following Furstenberg's theorem on positive Lyapunov exponent for products of random SL$(2, \mathbb R)$ matrices, that the one dimensional random Schr\"odinger operator has Anderson localization at arbitrary disorder. This…
We provide an analytic theory of Anderson localization on a lattice with a weak short-range correlated disordered potential. Contrary to the general belief we demonstrate that even next-neighbor statistical correlations in the potential can…
The phenomenon of localization is usually accompanied with the presence of quenched disorder. To what extent disorder is necessary for localization is a well-known open problem. In this paper, we prove the instability of localization in…
An ac field, tuned exactly to resonance with the Stark ladder in an ideal tight binding lattice under strong dc bias, counteracts Wannier-Stark localization and leads to the emergence of extended Floquet states. If there is random disorder,…
In disordered systems, our present understanding of the Anderson transition is hampered by the possible presence of interactions between particles. We demonstrate that in boson gases, even weak interactions deeply alter the very nature of…
Embedded solitons are exceptional modes in nonlinear-wave systems with the propagation constant falling in the system's propagation band. An especially challenging topic is seeking for such modes in nonlinear dynamical lattices (discrete…
Numerical approaches to Anderson localization face the problem of having to treat large localization lengths while being restricted to finite system sizes. We show that by finite-size scaling of the probability distribution of the local…
In the present paper we consider the quintic defocusing nonlinear Schr\"odinger equation in presence of a disordered random potential and we analyze the effects of the quintic nonlinearity on the Anderson localization of the solution. The…
In previous studies, the propagation of localized pulses (solitons, rogue waves and breathers) in electrical transmission lines has been studied. In this work, we extend this study to explore the transmission of positon solutions or…
We have studied the effect of a random superconducting order parameter on the localization of quasi-particles, by numerical finite size scaling of the Bogoliubov-de Gennes tight-binding Hamiltonian. Anderson localization is obtained in d=2…
We propose an experimental setup for studying the Anderson localization of light in the continuous transverse spatial degrees of freedom of the photons. This physical phenomenon can be observed in the transverse profile of a paraxial and…
We rigorously analyse the correspondence between the one-dimensional standard Anderson model and a related classical system, the `kicked oscillator' with noisy frequency. We show that the Anderson localization corresponds to a parametric…
Bloch wavefunctions in crystals experience localization within the bulk when disorder is introduced, a phenomenon commonly known as Anderson localization. This effect is considered universal, being applicable to all types of waves, quantum…
We present a method to demonstrate Anderson localization in an optically induced randomized potential. By usage of computer controlled spatial light modulators, we are able to implement fully randomized nondiffracting beams of variable…
In this paper, we prove Anderson localization for a hierarchical Anderson-Bernoulli model on lattice with arbitrary dimension, where the potential is characterized by a geometric hierarchical structure combined with fluctuations induced by…
We conduct a numerical investigation into wave propagation and localization in one-dimensional lattices subject to nonlinear disorder, focusing on cases with fixed input conditions. Utilizing a discrete nonlinear Schr\"odinger equation with…
Anderson localization is predicted to enhance the critical temperature of disordered superconductors. Despite a huge body of theoretical work based on non-linear sigma models, experiments are lacking to understand correlated electrons in…