Related papers: Short-distance wavefunction statistics in one-dime…
We present a perturbative approach to disordered systems in one spatial dimension that accesses the full range of phase disorder and clarifies the connection between localization and phase information. We consider a long chain of…
We study a one-dimensional model of disordered electrons (also relevant for random spin chains), which exhibits a delocalisation transition at half-filling. Exact probability distribution functions for the Wigner time and transmission…
We show, using quasi-exact numerical simulations, that Anderson localization of one-dimensional particles in a disordered potential survives in the presence of attractive interaction between particles. The localization length of the…
We study Anderson localization in two-dimensional systems with purely off-diagonal disorder. Localization lengths are computed by the transfer-matrix method and their finite-size and scaling properties are investigated. We find various…
A self-consistent theory of the frequency dependent diffusion coefficient for the Anderson localization problem is presented within the tight-binding model of non-interacting electrons on a lattice with randomly distributed on-site energy…
We investigate dynamical scaling properties of the 1D tight-binding Anderson model with a weak diagonal disorder, by means of the spreading of a wave packet. In the absence of disorder, and more generally in the ballistic regime, the…
We analyze the conductance distribution function in the one-dimensional Anderson model of localization, for arbitrary energy. For energy at the band center the distribution function deviates from the universal form assumed in…
In this paper, the statistical properties of Newton s method algorithm output in a specific case have been studied. The relative frequency density of this sample converges to a well-defined function, prompting us to explore its…
The one-dimensional (1d) Anderson model (AM) has statistical anomalies at any rational point $f=2a/\lambda_{E}$, where $a$ is the lattice constant and $\lambda_{E}$ is the de Broglie wavelength. We develop a regular approach to anomalous…
The localization properties of eigenfunctions for two interacting particles in the one-dimensional Anderson model are studied for system sizes up to $N=5000$ sites corresponding to a Hilbert space of dimension $\approx 10^7$ using the Green…
We present a full analytical solution for the localisation length in the one-dimensional Anderson model with weak diagonal disorder in the vicinity of the band centre. The results are obtained with the Hamiltonian map approach that turns…
We study Anderson localization in graphene with short-range disorder using the real-space Kubo-Greenwood method implemented on graphics processing units. Two models of short-range disorder, namely, the Anderson on-site disorder model and…
We investigate Anderson localization on various 1D structures having flat bands. The main focus is on the scaling laws obeyed by the localization length at weak disorder in the vicinity of flat-band energies. A careful distinction is made…
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…
A formalism is presented for analytically obtaining the probability density function, (P_{n}(s)), for the random distance (s) between two random points in an (n)-dimensional spherical object of radius (R). Our formalism allows (P_{n}(s)) to…
In the weak disordered regime we provide analytical expressions for the electron localization lengths in quasi-one dimensional (Q1D) disordered quantum wire with hard wall and periodic boundary conditions. They are exact up to order $W^2$…
We consider Anderson localization and the associated metal-insulator transition for non-interacting fermions in D = 1, 2 space dimensions in the presence of spatially correlated on-site random potentials. To assess the nature of the…
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 establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional…
Localization of wave functions in disordered systems can be characterized by the Lyapunov exponent, which is zero in the extended phase and nonzero in the localized phase. Previous studies have shown that this exponent is an analytic…