Related papers: Optimal Wegner estimates for random Schroedinger o…
For Schr\"{o}dinger type operators in one dimension, we consider the relationship between the convergence rate and the regularity for initial data. By establishing the associated frequency-localized maximal estimates, we prove sharp results…
Using an extension of the H\"ormander product of distributions, we obtain an intrinsic formulation of one-dimensional Schr\"odinger operators with singular potentials. This formulation is entirely defined in terms of standard {\it Schwartz}…
We give sufficient conditions for essential self-adjointness of magnetic Schr\"odinger operators on locally finite graphs. Two of the main theorems of the present paper generalize recent results of Torki-Hamza.
We consider a class of ensembles of lattice Schr\"odinger operators with deterministic random potentials, including quasi-periodic potentials with Diophantine frequencies, depending upon an infinite number of parameters in an auxiliary…
We consider multi-dimensional Schr\"odinger operators with a weak random perturbation distributed in the cells of some periodic lattice. In every cell the perturbation is described by the translate of a fixed abstract operator depending on…
This paper studies the Schr\"odinger operator with Morse potential on a right half line [u, \infty) and determines the Weyl asymptotics of eigenvalues for constant boundary conditions. It obtains information on zeros of the Whittaker…
The Wegner orbital model is a class of random operators introduced by Wegner to model the motion of a quantum particle with many internal degrees of freedom (orbitals) in a disordered medium. We consider the case when the matrix potential…
In this paper we prove stable determination of an inverse boundary value problem associated to a magnetic Schr\"odinger operator assuming that the magnetic and electric potentials are essentially bounded and the magnetic potentials admit a…
In the context of a weighted graph with vertex set $V$ and bounded vertex degree, we give a sufficient condition for the essential self-adjointness of the operator $\Delta_{\sigma}+W$, where $\Delta_{\sigma}$ is the magnetic Laplacian and…
In this paper, we study Strichartz estimates for the Schr\"odinger equation on a metric cone $X$, where $X=C(Y)=(0,\infty)_r\times Y$ and the cross section $Y$ is a $(n-1)$-dimensional closed Riemannian manifold $(Y,h)$. For the metric $g$…
We present an integral formulation of the vacuum energy of Schr\"odinger operators on finite metric graphs. Local vertex matching conditions on the graph are classified according to the general scheme of Kostrykin and Schrader. While the…
Boundedness of wave operators for Schr\"odinger operators in one space dimension for a class of singular potentials, admitting finitely many Dirac delta distributions, is proved. Applications are presented to, for example, dispersive…
We consider the problem of generating uniformly random partitions of the vertex set of a graph such that every piece induces a connected subgraph. For the case where we want to have partitions with linearly many pieces of bounded size, we…
In this article, we study the Schr\"odinger operator for a large class of periodic potentials with the symmetry of a hexagonal tiling of the plane. The potentials we consider are superpositions of localized potential wells, centered on the…
In this paper, we consider the Schr\"{o}dinger operators on $ \ell^{2}(\N) $, defined for all $ x\in\mathbb{T} $ by \begin{equation} (H(x)u)_n = u_{n+1} + u_{n-1} + \lambda f(2^{n} x) u_n, \quad \text{for } n \geq 0,\notag \end{equation}…
We consider random Schr\"odinger operators with Dirichlet boundary conditions outside lattice approximations of a smooth Euclidean domain and study the behavior of its lowest-lying eigenvalues in the limit when the lattice spacing tends to…
We develop a general approach to study three-dimensional Schroedinger operators with confining potentials depending on the distance to a surface. The main idea is to apply parallel coordinates based on the surface but outside its cut locus…
We study the behavior of averages for functions defined on finite graphs $G$, in terms of the Hardy-Littlewood maximal operator $M_G$. We explore the relationship between the geometry of a graph and its maximal operator and prove that $M_G$…
By suitably extending a Feynman-Kac formula of Simon [Canadian Math. Soc. Conf. Proc, 28 (2000), 317-321], we study one-parameter semigroups generated by (the negative of) rather general Schroedinger operators, which may be unbounded from…
We consider the Schr\"odinger operator with a periodic potential on a quasi 1D continuous periodic model of armchair nanotubes in $\R^3$ in a uniform magnetic field (with amplitude $B\in \R$), which is parallel to the axis of the nanotube.…