相关论文: Regularity of the density of states for random Dir…
We prove that the the density of states measure (DOSm) for random Schr\"odinger operators on $\mathbb{Z}^d$ is weak-$^*$ H\"older-continuous in the probability measure. The framework we develop is general enough to extend to a wide range of…
We study Schroedinger operators with a random potential of alloy type. The single site potentials are allowed to change sign. For a certain class of them we prove a Wegner estimate. This is a key ingredient in an existence proof of pure…
We consider one-dimensional random Schr\"odinger operators with a background potential, arising in the inverse problem of scattering. We study the influence of the background potential on the essential spectrum of the random Schr\"odinger…
We obtain a bound on the expectation of the spectral shift function for alloy-type random Schr\"odinger operators on $\mathbb{R}^d$ in the region of localisation, corresponding to a change from Dirichlet to Neumann boundary conditions along…
We establish the Anderson localization and exponential dynamical localization for a class of quasi-periodic Schr\"odinger operators on $\mathbb{Z}^d$ with bounded or unbounded Lipschitz monotone potentials via multi-scale analysis based on…
We review recent and give some new results on the spectral properties of Schroedinger operators with a random potential of alloy type. Our point of interest is the so called Wegner estimate in the case where the single site potentials…
We study spectra of Schr\"odinger operators on $\RR^d$. First we consider a pair of operators which differ by a compactly supported potential, as well as the corresponding semigroups. We prove almost exponential decay of the singular values…
We investigate some bounds for the density of states in the pure point regime for the random Schr\"{o}dinger operators $H^{\omega}=-\Delta+\displaystyle\sum_{n\in\mathbb{Z}^d}a_nq_n(\omega)$, acting on $\ell^2(\mathbb{Z}^d)$, where…
We consider the $d$-dimensional Anderson model, and we prove the density of states is locally analytic if the single site potential distribution is locally analytic and the disorder is large. We employ the random walk expansion of…
Electronic properties of amorphous or non-crystalline disordered solids are often modelled by one-particle Schroedinger operators with random potentials which are ergodic with respect to the full group of Euclidean translations. We give a…
In this paper we generalize and improve results proven for acoustic operators in \cite{jmp,long}. It deals with the behavior of the integrated density of states of random divergence operators of the form…
We study spectral properties of random operators in the general setting of groupoids and von Neumann algebras. In particular, we establish an explicit formula for the canonical trace of the von Neumann algebra of random operators and define…
The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schr{\"o}dinger operator with magnetic field and a random potential which may be…
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 that, for a density of disorder $\rho$ small enough, a certain class of discrete random Schr\"odinger operators on $\Z^d$ with diluted potentials exhibits a Lifschitz behaviour from the bottom of the spectrum up to energies at a…
We prove the existence and establish the Lifschitz singularity of the integrated density of states for certain random Hamiltonians $H^\omega=H_0+V^\omega$ on fractal spaces of infinite diameter. The kinetic term $H_0$ is given by…
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 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 construct random Schr\"odinger operators, called Anderson Hamiltonians, with Dirichlet and Neumann boundary conditions for a fairly general class of singular random potentials on bounded domains. Furthermore, we construct the integrated…
We study spectral properties of Schr\"odinger operators with random potentials of alloy type on $L^2(\RR)$ and their restrictions to finite intervals. A Wegner estimate for non-negative single site potentials with small support is proven.…