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The realization that electron localization in disordered systems (Anderson localization) is ultimately a wave phenomenon has led to the suggestion that photons could be similarly localized by disorder. This conjecture attracted wide…
We review the present status of the Anderson transition in the spectrum of the Dirac operator of QCD-like theories on the lattice. Localized modes at the low-end of the spectrum have been found in SU(2) Yang-Mills theory with overlap and…
Localization of wavefunctions is arguably the most familiar effect of disorder in quantum systems. It has been recently argued [[V. Khemani, R. Nandkishore, and S. L. Sondhi, Nature Physics, 11, 560 (2015)] that, contrary to naive…
Anderson localization is a general phenomenon that applies to a variety of disordered physical systems. Recently, a novel manifestation of Anderson localization for wave packets launched with a finite average velocity was proposed, the…
A major challenge in quantum optics and quantum information technology is to enhance the interaction between single photons and single quantum emitters. Highly engineered optical cavities are generally implemented requiring nanoscale…
The self-consistent theory of Anderson localization of quantum particles or classical waves in disordered media is reviewed. After presenting the basic concepts of the theory of Anderson localization in the case of electrons in disordered…
The optical absorption of a single spherical semiconductor quantum dot in an electrical field is studied taking into account the nonlocal coupling between the field of the light and the polarizability of the semiconductor. These nonlocal…
We consider diagonal disordered one-dimensional Anderson models with an underlying periodicity. We assume the simplest periodicity, i.e., we have essentially two lattices, one that is composed of the random potentials and the other of…
In an Anderson localized system, a quantum particle with a nonzero initial velocity returns, on average, to its origin. This recently discovered behavior is known as the quantum boomerang effect. Time reversal invariance was initially…
The effects of dynamic localization in a solid-state system -- a quantum dot -- are considered. The theory of weak dynamic localization is developed for non-interacting electrons in a closed quantum dot under arbitrary time-dependent…
Anderson localization, i.e. the suppression of diffusion in lattices with random or incommensurate disorder, is a fragile interference phenomenon which is spoiled out in the presence of dephasing effects or fluctuating disorder. As a…
We present a self-consistent theory of Anderson localization that yields a simple algorithm to obtain \emph{typical local density of states} as an order parameter, thereby reproducing the essential features of a phase-diagram of…
By employing Random Matrix Theory (RMT) and first-principle calculations, we investigated the behavior of Anderson localization in 1D, 2D and 3D systems characterized by a varying disorder. In particular, we considered random binary layer…
We investigate the dynamics of a quantum particle in disordered tight-binding models in one and two dimensions which are exceptions to the common wisdom on Anderson localization, in the sense that the localization length diverges at some…
We consider a random time evolution operator composed of a circuit of random unitaries coupling even and odd neighboring spins on a chain in turn. In spirit of Floquet evolution, the circuit is time-periodic; each timestep is repeated with…
Anderson localization1 in a random system is sensitive to a distance dependence of the excitation transfer amplitude V(r). If V(r) decreases with the distance r slower than 1/r^d in a d-dimensional system then all excitations are…
A recent development in studies of random non-Hermitian quantum systems is reviewed. Delocalization was found to occur under a sufficiently large constant imaginary vector potential even in one and two dimensions. The phenomenon has a…
We theoretically investigate the effects of atomic defect related short-range disorders and electron-electron interactions on Anderson type localization and the magnetic properties of hexagonal armchair graphene quantum dots using an…
We report on phenomenon of Anderson-type localization of walking solitons in optical lattices with random frequency modulation, manifested as dramatic enhancement of soliton trapping probability on lattice inhomogeneities with growth of the…
Disorder-induced Anderson localization in quasiparticle transport is a challenging problem to address, even more so in the presence of dissipation as the symptoms of disorder-induced localization are very closely simulated by the absorption…