Related papers: Analytic and numerical toolkit for the Anderson mo…
We describe a large disorder renormalization group (LDRG) method for the Anderson model of localization in one dimension which decimates eigenstates based on the size of their wavefunctions rather than their energy. We show that our LDRG…
We develop a cluster typical medium theory to study localization in disordered electronic systems. Our formalism is able to incorporate non-local correlations beyond the local typical medium theory in a systematic way. The cluster typical…
We study Anderson localization in disordered tight-binding models on hyperbolic lattices. Such lattices are geometries intermediate between ordinary two-dimensional crystalline lattices, which localize at infinitesimal disorder, and Bethe…
We investigate the equilibration of a small isolated quantum system by means of its matrix of asymptotic transition probabilities in a preferential basis. The trace of this matrix is shown to measure the degree of equilibration of the…
We provide evidence that as a general rule Anderson localization effects become weaker as the degree of differentiability of the disordered potential increases. In one dimension a band of metallic states exists provided that the disordered…
Algebraic and geometric mean density of states in disordered systems may reveal properties of electronic localization. In order to understand the topological phases with disorder in two dimensions, we present the calculated density of…
We developed an analytic theory of inhomogeneous superconducting pairing in strongly disordered materials, which are moderately close to superconducting-insulator transition. Single-electron eigenstates are assumed to be Anderson-localized,…
We examine the localization properties of the Anderson Hamiltonian with additional off-diagonal disorder using the transfer-matrix method and finite-size scaling. We compute the localization lengths and study the metal-insulator transition…
An application of an effective numerical algorithm for solving eigenvalue problems which arise in modelling electronic properties of quantum disordered systems is considered. We study the electron states at the localization-delocalization…
Using the phenomenological expression for the level spacing distribution with only one parameter, $0 \leq \beta \leq \infty$, covering all regimes of chaos and complexity in a quantum system, we show that transport properties of the…
The nearest-neighbor level spacing distribution is numerically investigated by directly diagonalizing disordered Anderson Hamiltonians for systems of sizes up to 100 x 100 x 100 lattice sites. The scaling behavior of the level statistics is…
We investigate how free probability allows us to approximate the density of states in tight binding models of disordered electronic systems. Extending our previous studies of the Anderson model in neighbor interactions [J. Chen et al.,…
The Anderson model serves to study the absence of wave propagation in a medium in the presence of impurities, and is one of the most studied examples in the theory of quantum disordered systems. In these notes we give a review of the…
We show that the Anderson model has a transition from localization to delocalization at exactly 2 dimensional growth rate on antitrees with normalized edge weights which are certain discrete graphs. The kinetic part has a one-dimensional…
Anderson localisation is an important phenomenon arising in many areas of physics, and here we explore it in the context of quantum information devices. Finite dimensional spin chains have been demonstrated to be important devices for…
We study numerically the localization properties of eigenstates in a one-dimensional random lattice described by a non-Hermitian disordered Hamiltonian, where both the disorder and the non-Hermiticity are inserted simultaneously in the…
Anderson localization is a consequence of coherent interference of multiple scattering events in the presence of disorder, which leads to an exponential suppression of the transmission. The decay of the transmission is typically probed at a…
We show that the recently developed self-consistent theory of Anderson localization with a position-dependent diffusion coefficient is in quantitative agreement with the supersymmetry approach up to terms of the order of $1/g_0^2$ (with…
We study Anderson localization in quasi--one--dimensional disordered wires within the framework of the replica $\sigma$--model. Applying a semiclassical approach (geodesic action plus Gaussian fluctuations) recently introduced within the…
A statistical theory of the coupling between a quantum emitter and Anderson-localized cavity modes is presented based on a dyadic Green's function formalism. The probability of achieving the strong light-matter coupling regime is extracted…