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Motivated by recent advances in the realization of Truchet-tiling structures in molecular networks and metal-organic frameworks, we investigate the wave localization issue in this kind of structure. We introduce an electron model based on…
In this note we show that, a simple combination of deep results in the theory of random Schr\"odinger operators yields a quantitative estimate of the fact that the localization centers become far apart, as corresponding energies are close…
We apply a recently developed approach (Liaw 2013) to study the existence of extended states for the three dimensional discrete random Schroedinger operator at small disorder. The conclusion of delocalization at small disorder agrees with…
We investigate the localization of electronic states in the integer quantum Hall effect using a magnetic localization landscape (MLL) approach. By studying a continuum Schr\"odinger model with disordered electrostatic potential, we…
Results of large-scale numerical simulations are reported on the Anderson localization in a two-dimensional square lattice tight-binding model with random flux. Localization lengths, fluctuations of the conductance, and the density of…
We prove localization (near the bottom of the spectrum) for certain non-stationary variants of the Anderson model in three dimensions. More specifically, we prove a Wegner estimate, which implies localization by existing work. Two key…
Using the method of energy-level statistics, the localization properties of electrons moving in two dimensions in the presence of a perpendicular random magnetic field and additional random disorder potentials are investigated. For this…
We demonstrate, by solving numerically the time-dependent Schroedinger equation, the physical character of electron localization in a disordered two-dimensional lattice. We show, in agreement with the prediction of P. W. Anderson, that the…
This paper concerns the numerical approximation of low-energy eigenstates of the linear random Schr\"odinger operator. Under oscillatory high-amplitude potentials with a sufficient degree of disorder it is known that these eigenstates…
We survey some aspects of the theory of the integrated density of states (IDS) of random Schroedinger operators. The first part motivates the problem and introduces the relevant models as well as quantities of interest. The proof of the…
We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger liquid model. We demonstrate that the notion of weak localization is applicable to the strongly correlated…
Electron transport through disordered quasi one-dimensional quantum systems is studied. Decoherence is taken into account by a spatial distribution of virtual reservoirs, which represent local interactions of the conduction electrons with…
We prove Lifshitz behavior at the bottom of the spectrum for non--negative random potentials, i.\,e.\ show that the IDS is exponentially small at low energies. The theory is developed for the breather potential and generalized to all…
The Wigner localization is an electron phase at low densities when the electrons are sharply localized around equilibrium positions. The simulation of the Wigner localization phenomenon requires careful treatment of the many-body…
We continue the investigations of Kirsch, Metzger and the second-named author [J. Stat. Phys. 143, 1035--1054 (2011)] on spectral properties of a certain type of random block operators. In particular, we establish an alternative version of…
The present paper is devoted to the study of spectral properties of random Schroedinger operators. Using a finite section method for Toeplitz matrices, we prove a Wegner estimate for some alloy type models where the single site potential is…
We consider discrete one-dimensional Schr\"odinger operators with random potentials obtained via a block code applied to an i.i.d. sequence of random variables. It is shown that, almost surely, these operators exhibit spectral and dynamical…
We develop a new approach for the Anderson localization problem. The implementation of this method yields strong numerical evidence leading to a (surprising to many) conjecture: The two dimensional discrete random Schroedinger operator with…
We study spectral properties of ergodic random Schr\"odinger operators on $L^2 (\RR^d)$. The density of states is shown to exist for a certain class of alloy type potentials with single site potentials of changing sign. The Wegner estimate…
We consider the spectral and dynamical properties of quantum systems of $n$ particles on the lattice $\Z^d$, of arbitrary dimension, with a Hamiltonian which in addition to the kinetic term includes a random potential with iid values at the…