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Recent advances in transport properties measurements of disordered materials and lattice simulations, using superconducting qubits, have rekindled interest in Anderson localization, motivating our study of highly disordered quantum…

In this paper, we discuss the transport phenomena of electromagnetic waves in a two-dimensional random system which is composed of arrays of electrical dipoles, following the model presented earlier by Erdogan, et al. (J. Opt. Soc. Am. B…

We present analytical results on transport properties of many-mode waveguides with randomly stratified disorder having long-range correlations. To describe such systems, the theory of 1D transport recently developed for a correlated…

To better understand the temporal characteristics and the lifetime of fluctuations in stochastic processes in networks, we investigated diffusive persistence in various graphs. Global diffusive persistence is defined as the fraction of…

We study the effect of a resonant frequency disorder on the eigenstates and the transport of magnetic energy in a two-dimensional (square) array of split-ring resonators (SRRs). In the absence of disorder, we find the dispersion relation of…

Anderson localisation -- the inhibition of wave propagation in disordered media -- is a surprising interference phenomenon which is particularly intriguing in two-dimensional (2D) systems. While an ideal, non-interacting 2D system of…

Subradiance is a phenomenon where coupled emitters radiate light at a slower rate than independent ones. While its observation was first reported in disordered cold atom clouds, ordered subwavelength arrays of emitters have emerged as…

We present a numerical study on the light transport properties which are modulated by the disorder strength in quasi-one-dimensional disordered waveguide which consists of periodically arranged scatterers with random dielectric constant.…

We investigate the dynamic behavior of lattices with disorder introduced through non-local network connections. Inspired by the Watts-Strogatz small-world model, we employ a single parameter to determine the probability of local connections…

Topic of the thesis is a theoretical description of the ultracold atomic gases in one- and two-dimensional optical lattices in the presence of the disorder leading to the Anderson localization. The disorder is created by interaction of the…

Charge transport in disordered two-dimensional (2D) systems showcases a myriad of unique phenomenologies that highlight different aspects of the underlying quantum dynamics. Electrons in such systems undergo a crossover from ballistic…

We study a 2-dimensional model for an antidot periodic superlattice with perturbed positions of the antidots. To do so we use a quasiperiodic LG model obtained from a 3-dimensional billiard model. Our results show that infinite drifting…

We study the propagation of a density perturbation in a weakly interacting boson gas confined on a lattice and in the presence of square dimerized impurities. Such a two-dimensional random-dimer model (2D-DRDM), previously introduced in…

We present first analytical results on transport properties of many-mode waveguides with rough surfaces having long-range correlations. We show that propagation of waves through such waveguides reveals a quite unexpected phenomena of a…

We develop an analytical theory for diffusive random lasers by coupling the transport theory of the disordered medium to the semiclassical laser rate equations, accounting for (coherent) stimulated and (incoherent) spontaneous emission.…

We investigate light transport in three-dimensional disordered media composed of irregular dielectric particles using large scale full-wave simulations. For subwavelength particles with size parameter $kr \approx 1$ and high refractive…

We study the effect of disorder on the particle density evolution in a classical Hamiltonian driven lattice setup. If the disorder is localized within a finite sub-domain of the lattice, the emergence of strong tails in the density…

In this work, we investigate numerically the transport properties of a 2D complex plasma crystal using diffusion of coplanar dust lattice waves. In the limit where the Hamiltonian interactions can be decoupled from the non-Hamiltonian…

Structural correlations in disordered media are known to affect significantly the propagation of waves. In this article, we theoretically investigate the transport and localization of light in 2D photonic structures with short-range…

Two-dimensional networks of ordered quantum dots beyond the percolation threshold are studied, as typical example of conducting nanostructures with quenched random disorder. Theory predicts anomalous diffusion with stretched-exponential…