Related papers: Analytic and numerical toolkit for the Anderson mo…
We consider the notion of equilibration for an isolated quantum system exhibiting Anderson localization. The system is assumed to be in a pure state, i.e., described by a wave-function undergoing unitary dynamics. We focus on the simplest…
This work proposes a very simple random matrix model, the Flip Matrix Model, liable to approximate the behavior of a two dimensional electron in a weak random potential. Its construction is based on a phase space analysis, a suitable…
Single-particle transport in disordered potentials is investigated on scales below the localization length. The dynamics on those scales is concretely analyzed for the 3-dimensional Anderson model with Gaussian on-site disorder. This…
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…
We study the interplay of disorder and interaction effects including bosonic degrees of freedom in the framework of a generic one-dimensional transport model, the Anderson-Edwards model. Using the density-matrix renormalization group…
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…
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…
The existence of Anderson localization, characterized by vanishing diffusion due to strong disorder, has been demonstrated in numerous ways. A systematic approach based on the Anderson quantum model of the Fermi gas in random lattices that…
The statistical properties of overlap sums of groups of four eigenfunctions of the Anderson model for localization as well as combinations of four eigenenergies are computed. Some of the distributions are found to be scaling functions, as…
We study analytically and numerically the Anderson model in one dimension with "stealthy" disorder, defined as having a power spectrum that vanishes in a continuous band of wave numbers. Motivated by recent studies on the optical…
Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary…
We study the dependence on the spatial dimensionality of different quantities relevant in the description of the Anderson transition by combining numerical calculations in a $3 \leq d \leq 6$ disordered tight binding model with theoretical…
We theoretically study the Anderson localization of a matter wave packet in a one-dimensional disordered potential. We develop an analytical model which includes the initial phase-space density of the matter wave and the spectral broadening…
We rigorously analyse the correspondence between the one-dimensional standard Anderson model and a related classical system, the `kicked oscillator' with noisy frequency. We show that the Anderson localization corresponds to a parametric…
In the present note we show dynamical localization for an Anderson model with missing sites in a discrete setting at the bottom of the spectrum in arbitrary dimension $d$. In this model, the random potential is defined on a relatively dense…
We present the first rigorous result on Anderson localization for interacting systems of quantum particles subject to a deterministic (e.g., almost periodic) disordered external potential. For a particular class of deterministic, fermionic,…
In the one-dimensional Anderson model the eigenstates are localized for arbitrarily small amounts of disorder. In contrast, the Harper model with its quasiperiodic potential shows a transition from extended to localized states. The…
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…
We show that, in contrast to immediate intuition, Anderson localization of noninteracting particles induced by a disordered potential in free space can increase (i.e., the localization length can decrease) when the particle energy…
Analytical complexity of quantum wavefunction whose argument is extended into the complex plane provides an important information about the potentiality of manifesting complex quantum dynamics such as time-irreversibility, dissipation and…