Related papers: Classical Representation of the 1D Anderson Model
A new method is developed for the study of transport properties of 1D models with random potentials. It is based on an exact transformation that reduces discrete Schr\"odinger equation in the tight-binding model to a two-dimensional…
We demonstrate that by considering disordered single-particle Hamiltonians (or their random matrix versions) on ultrametric spaces one can generate an interesting class of models exhibiting Anderson metal-insulator transition. We use the…
We examine the localization properties of the three-dimensional (3D) Anderson Hamiltonian with off-diagonal disorder using the transfer-matrix method (TMM) and finite-size scaling (FSS). The nearest-neighbor hopping elements are chosen…
It is believed that the two-dimensional (2D) Anderson model exhibits localization for any nonzero disorder in the thermodynamic limit and it is also well known that the finite-size effects are considerable in the weak disorder limit. Here…
The Anderson model for independent electrons in a disordered potential is transformed analytically and exactly to a basis of random extended states leading to a variant of augmented space. In addition to the widely-accepted phase diagrams…
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…
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…
For the weakly interacting one-dimensional multi-particle Anderson model in the continuum space of configurations, we prove the spectral exponential and the strong dynamical localization. The results require the interaction amplitude to be…
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…
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…
Anderson localization has been a subject of intense studies for many years. In this context, we study numerically the influence of long-range correlated disorder on the localization behavior in one dimensional systems. We investigate the…
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 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…
We introduce a matrix-operator formulation of the Anderson model in d=2. In a single slice, we can then derive an analogy between our model and a standard random matrices problem. This enables us to construct and control the Green function…
In this paper, we developed a new parametrization method to calculate the localization length in one-dimensional Anderson model with diagonal disorder. This method can avoid the divergence difficulty encountered in the conventional methods,…
We calculated numerically the localization length of one-dimensional Anderson model with correlated diagonal disorder. For zero energy point in the weak disorder limit, we showed that the localization length changes continuously as the…
The effect of disorder on magnonic transport in low-dimensional magnetic materials is studied in the framework of a classical spin model. Numerical investigations give insight into scattering properties of the systems and show the existence…
A basis of Bloch waves, distorted locally by the random potential, is introduced for electrons in the Anderson model. Matrix elements of the Hamiltonian between these distorted waves are averages over infinite numbers of independent…
We consider two bidimensional random models characterised by the following features: a) their Hamiltonians are separable in polar coordinates and b) the random part of the potential depends either on the angular coordinate or on the radial…
The method proposed by the present authors to deal analytically with the problem of Anderson localization via disorder [J.Phys.: Condens. Matter {\bf 14} (2002) 13777] is generalized for higher spatial dimensions D. In this way the…