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In linear disordered systems Anderson localization makes any wave packet stay localized for all times. Its fate in nonlinear disordered systems is under intense theoretical debate and experimental study. We resolve this dispute showing that…
We investigate numerically the effect of the competition of disorder, nonlinearity, and boundaries on the Anderson localization of light waves in finite-size, one-dimensional waveguide arrays. Using the discrete Anderson - nonlinear…
We consider the transport of non-interacting electrons on two- and three-dimensional random Voronoi-Delaunay lattices. It was recently shown that these topologically disordered lattices feature strong disorder anticorrelations between the…
We review some recent (mostly ours) results on the Anderson localization of light and electron waves in complex disordered systems, including: (i) left-handed metamaterials, (ii) magneto-active optical structures, (iii) graphene…
We consider one-dimensional asymmetric exclusion processes with a simple attractive interaction, where the distance between consecutive particles is not allowed to exceed a certain limit and investigate the consequences of this coupling on…
Molecular materials have been studied as a potential platform for highly efficient transport such as exciton transport and quantum information spreading. However, one detrimental factor to transport efficiency is the inherent disorder of…
The effect of disorder on magnonic transport in low-dimensional magnetic materials is studied in the framework of a classical spin model. Numerical investigations give insight into scattering properties of the systems and show the existence…
We consider the problem of electron transport along a one-dimensional disordered multiple-scattering conductor, and study the electron density for all the electronic levels. A model is proposed for the reduced density matrix of the system…
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, 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…
The subject of this study is the long-time equilibration dynamics of a strongly disordered one-dimensional chain of coupled weakly anharmonic classical oscillators. It is argued that chaos in this system has a very particular spatial…
We study the chaotic behavior of multidimensional Hamiltonian systems in the presence of nonlinearity and disorder. It is known that any localized initial excitation in a large enough linear disordered system spreads for a finite amount of…
We investigate the propagation and scattering of highly nonlinear waves in disordered granular chains composed of diatomic (two-mass) units of spheres that interact via Hertzian contact. Using ideas from statistical mechanics, we consider…
The interplay between nonlinear effects and Anderson localization in disordered optical fibres1 has recently attracted great interest, and it is important in the action of random lasers in which closed multiple scattering loops have…
Planar wave trains are traveling wave solutions whose wave profiles are periodic in one spatial direction and constant in the transverse direction. In this paper, we investigate the stability of planar wave trains in reaction-diffusion…
Controlling the flow of energy in a random medium is a research frontier with a wide range of applications. As recently demonstrated, the effect of disorder on the transmission of optical beams, may be partially compensated by wavefront…
Diffusive transport is among the most common phenomena in nature [1]. However, as predicted by Anderson [2], diffusion may break down due to interference. This transition from diffusive transport to localization of waves should occur for…
Quantum degenerate gases trapped in optical lattices are ideal testbeds for fundamental physics because these systems are tunable, well characterized, and isolated from the environment. Controlled disorder can be introduced to explore…
Wave propagation in disordered media can be strongly modified by multiple scattering and wave interference. Ultimately the so-called Anderson-localized regime is reached when the waves become strongly confined in space. So far, Anderson…
It is widely believed that many-body localisation in one dimension is fragile and can be easily destroyed by thermal inclusions, however there are still many open questions regarding the stability of the localised phase and under what…