Related papers: Exponential Dynamical Localization for Random Word…
We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\"odinger operator which describes the quantum mechanics of an…
The purpose of this paper is to understand in more detail the shape of the eigenvectors of the random Schroedinger operator H = Delta+V. Here Delta is the discrete Laplacian and V is a random potential. It is well known that under certain…
We consider operators with random potentials on graphs, such as the lattice version of the random Schroedinger operator. The main result is a general bound on the probabilities of simultaneous occurrence of eigenvalues in specified distinct…
We study the localization of wave functions for one-dimensional Schr\"odinger Hamiltonians with random potentials $V(x)$ with short range correlations and large local fluctuations such that $\int\D{x} \smean{V(x)V(0)}=\infty$. A random…
We consider Schroedinger operators with a random potential of alloy type on infinite metric graphs which obey certain uniformity conditions. For single site potentials of fixed sign we prove that the random Schroedinger operator restricted…
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…
In this work we obtain the integrated density of states for the Schr\"{o}dinger operators with decaying random potentials acting on $\ell^2(\mathbb{Z}^d)$. We also study the asymptotic of the largest and smallest eigenvalues of its finite…
Proofs of localization for random Schr\"odinger operators with sufficiently regular distribution of the potential can take advantage of the fractional moment method introduced by Aizenman-Molchanov, or use the classical Wegner estimate as…
Recently, Aizenman and Warzel discovered a mechanism for the appearance of absolutely continuous spectrum for random Schroedinger operators on the Bethe lattice through rare resonances (resonant delocalization). We extend their analysis to…
This paper concerns spectral properties of linear Schr\"odinger operators under oscillatory high-amplitude potentials on bounded domains. Depending on the degree of disorder, we prove the existence of spectral gaps amongst the lowermost…
We consider discrete random Schr\"odinger operators on $\ell^2 (\mathbb{Z}^d)$ with a potential of discrete alloy-type structure. That is, the potential at lattice site $x \in \mathbb{Z}^d$ is given by a linear combination of independent…
We prove dynamical and spectral localization at all energies for the discrete generalized Anderson model via the Kunz-Souillard approach to localization. This is an extension of the original Kunz-Souillard approach to localization for…
In \cite{Lee:2006:schrod-converg}, when the spatial variable $x$ is localized, Lee observed that the Schr\"odinger maximal operator $e^{it\Delta}f(x)$ enjoys certain localization property in $t$ for frequency localized functions. In this…
We prove that for any {\it fixed} trigonometric polynomial potential satisfying a genericity condition, the spectrum of the two dimension periodic Schr\"odinger operator has finite multiplicity and the Fourier series of the eigenfunctions…
We study discrete random Schr\"odinger operators via the supersymmetric formalism. We develop a cluster expansion that converges at both strong and weak disorder. We prove the exponential decay of the disorder-averaged Green's function and…
We prove Anderson localization (AL) and dynamical localization in expectation (EDL, also known as strong dynamical localization) for random CMV matrices for arbitrary distribution of i.i.d. Verblunsky coefficients.
We consider Schr\"odinger operators on $L^2(R^d)$ with a random potential concentrated near the surface $R^{d_1}\times\{0\}\subset R^d $. We prove that the integrated density of states of such operators exhibits Lifshits tails near the…
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…
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 review recent results on localization for discrete alloy-type models based on the multiscale analysis and the fractional moment method, respectively. The discrete alloy-type model is a family of Schr\"odinger operators $H_\omega = -…