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We present a thorough study of the complexity of optical localized modes in two-dimensional disordered photonic crystals. Direct experimental measurements of complexity were made using an interferometric setup that allowed for extraction of…
Above the QCD chiral crossover temperature, the low-lying eigenmodes of the Dirac operator are localised, while moving up in the spectrum states become extended. This localisation/delocalisation transition has been shown to be a genuine…
The Anderson transition in three dimensions in a randomly varying magnetic flux is investigated in detail by means of the transfer matrix method with high accuracy. Both, systems with and without an additional random scalar potential are…
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 prove that a strongly disordered two-dimensional system localizes with a localization length given analytically. We get a scaling law with a critical exponent is $\nu=1$ in agreement with the Chayes criterion $\nu\ge 1$. The case we are…
Anderson localization transitions are a universal quantum phenomenon sensitive to the disorder and dimensionality of electronic systems. Over the past decades, this intriguing topic has inspired overwhelmingly more theoretical studies than…
We study Anderson localization of single particles in continuous, correlated, one-dimensional disordered potentials. We show that tailored correlations can completely change the energy-dependence of the localization length. By considering…
Anderson localization predicts that wave spreading in disordered lattices can come to a complete halt, providing a universal mechanism for {dynamical localization}. In the one-dimensional Hermitian Anderson model with uncorrelated diagonal…
We report a numerical investigation of the Anderson transition in two-dimensional systems with spin-orbit coupling. An accurate estimate of the critical exponent $\nu$ for the divergence of the localization length in this universality class…
The Anderson metal-insulator transition is a continuous phase transition driven by disorder. It remains a challenging problem to theoretically determine universal critical properties at the transition. The Anderson transition in a model…
The localization length has been derived for one-dimensional bi-layered structures with random perturbations in the refractive indices for each type of layers. Main attention is paid to the comparison between conventional materials and…
The Anderson model in one dimension is a quantum particle on a discrete chain of sites with nearest-neighbor hopping and random on-site potentials. It is a progenitor of many further models of disordered systems, and it has spurred numerous…
The three-dimensional Anderson model with a rectangular distribution of site disorder displays two distinct localization-delocalization transitions, against varying disorder intensity, for a relatively narrow range of Fermi energies. Such…
We study the interplay of disorder and interaction effects including bosonic degrees of freedom in the framework of a generic one-dimensional transport model, the Anderson-Edwards model. Using the density-matrix renormalization group…
We report improved numerical estimates of the critical exponent of the Anderson transition in Anderson's model of localization in $d=4$ and $d=5$ dimensions. We also report a new Borel-Pad\'e analysis of existing $\epsilon$ expansion…
We study the disorder-induced crossover between the two recently discovered thermalization slowing-down universality classes -- characterized by long- and short-range coupling -- in classical unitary circuits maps close to integrability. We…
The disorder induced metal--insulator transition is investigated in a three-dimensional simple cubic lattice and compared for the presence and absence of time-reversal and spin-rotational symmetry, i.e. in the three conventional symmetry…
We show that, in contrast to immediate intuition, Anderson localization of noninteracting particles induced by a disordered potential in free space can increase (i.e., the localization length can decrease) when the particle energy…
We study the effect of disorder in a holographic superconductor by introducing a quasi-periodic chemical potential. When the condensation of the superconductor is sufficiently small compared with the strength of disorder, we find that there…
We review our recent results on Anderson localization in systems of two interacting particles coupled by contact interactions. Based on an exact mapping to an effective single-particle problem, we numerically investigate the occurrence of…