Related papers: An eigensystem approach to Anderson localization
An analytical realization is suggested for the finite-size scaling algorithm based on the consideration of auxiliary quasi-1D systems. Comparison of the obtained analytical results with the results of numerical calculations indicates that…
We introduce an approach for exploring eigenvector localization phenomena for a class of (unbounded) selfadjoint operators. More specifically, given a target region and a tolerance, the algorithm identifies candidate eigenpairs for which…
We describe a way of detecting the location of localized eigenvectors of a linear system $Ax = \lambda x$ for eigenvalues $\lambda$ with $|\lambda|$ comparatively large. We define the family of functions $f_{\alpha}: \left\{1.2. \dots,…
We study the spatial structure of wave functions with exceptionally high local amplitudes in the Anderson model of localisation. By means of exact diagonalisations of finite systems, we obtain and analyse images of these wave functions: we…
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…
As part of condensed-matter physics, the field of Anderson localization concerns the study of conductance of electrons in a random medium. We summarize and explain the results obtained in "A new numerical approach to Anderson…
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…
In this paper we present a thorough study of transport, spectral and wave-function properties at the Anderson localization critical point in spatial dimensions $d = 3$, $4$, $5$, $6$. Our aim is to analyze the dimensional dependence and to…
We consider the multi-particle Anderson tight-binding model and prove that its lower spectral edge is non-random under some mild assumptions on the inter-particle interaction and the random external potential. We also adapt to the low…
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…
We develop a method for calculating the self-energy of a quantum impurity coupled to a continuous bath by stochastically generating a distribution of finite Anderson models that are solved by exact diagonalization, using the noninteracting…
We derive a field-theoretical representation for the moments of the eigenstates in the generalized Anderson model. The representation is exact and can be used for the Anderson model with generic non-random hopping elements in any…
We investigate the top of the spectrum of discrete Anderson Hamiltonians with correlated Gaussian noise in the large volume limit. The class of Gaussian noises under consideration allows for long-range correlations. We show that the largest…
We establish, through numerical calculations and comparisons with a recursive Green's function based implementation of the Landauer-B\"uttiker formalism, an efficient method for studying Anderson localization in quasi-one-dimensional and…
We review several techniques and ideas initiated by a remarkable work by Spencer [26], used and further developed in numerous subsequent researches. We also describe a relatively short and elementary derivation of the spectral and strong…
We study phenomena where some eigenvectors of a graph Laplacian are largely confined in small subsets of the graph. These localization phenomena are similar to those generally termed Anderson Localization in the Physics literature, and are…
We consider the multi-particle Anderson model on the lattice with infinite range but sub-exponentially decaying interaction and show the Anderson localization consisting of the spectral exponential and the strong dynamical localization. In…
Disorder can fundamentally modify the transport properties of a system. A striking example is Anderson localization, suppressing transport due to destructive interference of propagation paths. In inhomogeneous many-body systems, not all…
We prove the occurrence of Anderson localisation for a system of infinitely many particles interacting with a short range potential, within the ground state Hartree-Fock approximation. We assume that the particles hop on a discrete lattice…
This study investigates the entanglement properties of disordered free fermion systems undergoing an Anderson phase transition from a delocalized to a localized phase. The entanglement entropy is employed to quantify the degree of…