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We develop a numerical technique to study Anderson localization in interacting electronic systems. The ground state of the disordered system is calculated with quantum Monte-Carlo simulations while the localization properties are extracted…
Dyson insulators with random hoppings in a lattice approach localization faster compared to the usual Anderson insulators with site disorder. For even-$N$ lattice sites the Dyson insulators mimic topological insulators with a pseudo-gap at…
Localization of coherent propagating waves has been extensively studied over the years, primarily in homogeneous random media. However, significantly less attention has been given to wave localization in inhomogeneous systems, where the…
Disordered stealthy hyperuniform (SHU) two-phase media are a special subset of hyperuniform structures with novel physical properties due to their hybrid crystal-liquid nature. We have previously shown that the strong-contrast expansion of…
We frame the transverse Anderson localization of light in a one-dimensional disordered optical lattice in the language of localized propagating eigenmodes. The modal analysis allows us to explore localization behavior of a disordered…
We develop an alternative scaling approach to determine the criteria for Anderson localization in one-dimensional tight-binding models with random site energies having a bandwidth that decays as a power law in space, $H_{ij} \propto |i -…
Transverse Anderson localization of light allows localized optical-beam-transport through a transversely-disordered and longitudinally-invariant medium. Its successful implementation in disordered optical fibers recently resulted in the…
We discuss the localization behavior of localized electronic wave functions in the one- and two-dimensional tight-binding Anderson model with diagonal disorder. We find that the distributions of the local wave function amplitudes at fixed…
We study wave transmission through one-dimensional random nonlinear structures and predict a novel effect resulting from an interplay of nonlinearity and disorder. We reveal that, while weak nonlinearity does not change the typical…
We investigate the scaling properties of the two-dimensional (2D) Anderson model of localization with purely off-diagonal disorder (random hopping). In particular, we show that for small energies the infinite-size localization lengths as…
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…
Disorder can fundamentally modify the transport properties of a system. A striking example is Anderson localization, suppressing transport due to destructive interference of propagation paths. In inhomogeneous many-body systems, not all…
Hyperuniform disordered photonic materials (HDPM) are spatially correlated dielectric structures with unconventional optical properties. They can be transparent to long-wavelength radiation while at the same time have isotropic band gaps in…
In this paper, we propose a one-dimensional disordered plasmonic structure composed of a graphene single layer placed on a random grating composed of InAs. The propagation of a plasmonic wave through this structure is investigated…
We introduce a two-dimensional generalisation of the quasiperiodic Aubry-Andr\'e model. Even though this model exhibits the same duality relation as the one-dimensional version, its localisation properties are found to be substantially more…
We introduce the mode area probability density function (MA-PDF) as a powerful tool to study transverse Anderson localization (TAL), especially for highly disordered optical fibers. The MA-PDF encompasses all the relevant statistical…
Disordered transverse Anderson localizing optical fibers have shown great promise in various applications from image transport to random lasing. Their success is due to their novel waveguiding behavior, which is enabled by the transverse…
We show in microwave measurements and computer simulations that the contribution of each eigenchannel of the transmission matrix to the density of states (DOS) is the derivative with angular frequency of a composite phase shift. The…
Anderson localization is a ubiquitous interference phenomenon in which waves fail to propagate in a disordered medium. Unlike in a classical resonator, satisfying the favorable condition for the interference in a disordered medium is truly…
Diffusion has been widely used to describe a random walk of particles or waves, and it requires only one parameter -- the diffusion constant. For waves, however, diffusion is an approximation that disregards the possibility of interference.…