Related papers: Level repulsion for Schroedinger operators with si…

We consider decaying oscillatory perturbations of periodic Schr\"odinger operators on the half line. More precisely, the perturbations we study satisfy a generalized bounded variation condition at infinity and an $L^p$ decay condition. We…

We discuss Schr\"odinger operators on a half-line with decaying oscillatory potentials, such as products of an almost periodic function and a decaying function. We provide sufficient conditions for preservation of absolutely continuous…

We study the level statistics of one-dimensional Schr\"odinger operator with random potential decaying like $x^{-\alpha}$ at infinity. We consider the point process $\xi_L$ consisting of the rescaled eigenvalues and show that : (i)(ac…

This paper deals with general structural properties of one-dimensional Schr"odinger operators with some absolutely continuous spectrum. The basic result says that the omega limit points of the potential under the shift map are…

We prove asymptotics of the Christoffel function, $\lambda_L(\xi)$, of a continuum Schr\"odinger operator for points in the interior of the essential spectrum under some mild conditions on the spectral measure. It is shown that…

This paper presents a thorough analysis of 1-dimensional Schroedinger operators whose potential is a linear combination of the Coulomb term 1/r and the centrifugal term 1/r^2. We allow both coupling constants to be complex. Using natural…

We consider Schr\"odinger operators with potentials satisfying a generalized bounded variation condition at infinity and an $L^p$ decay condition. This class of potentials includes slowly decaying Wigner--von Neumann type potentials…

This paper presents the spectral analysis of 1-dimensional Schroedinger operator on the half-line whose potential is a linear combination of the Coulomb term 1/r and the centrifugal term 1/r^2. The coupling constants are allowed to be…

We consider Schr\"odinger operators on the real line with limit-periodic potentials and show that, generically, the spectrum is a Cantor set of zero Lebesgue measure and all spectral measures are purely singular continuous. Moreover, we…

I prove that the spectrum of a skew-shift Schr\"odinger operator contains larges interval in the semi-classical regime. In the semi-classical limit, these intervals approach the range of the potential.

We consider a family of random Schr\"odinger operators on the discrete strip with decaying random $\ell^2$ matrix potential. We prove that the spectrum is almost surely pure absolutely continuous, apart from random, possibly embedded…

The norm resolvent convergence of discrete Schr\"odinger operators to a continuum Schr\"odinger operator in the continuum limit is proved under relatively weak assumptions. This result implies, in particular, the convergence of the spectrum…

We show that a large class of limit-periodic Schr\"odinger operators has purely absolutely continuous spectrum in arbitrary dimensions. This result was previously known only in dimension one. The proof proceeds through the non-perturbative…

We consider ergodic families of Schr\"odinger operators over base dynamics given by strictly ergodic subshifts on finite alphabets. It is expected that the majority of these operators have purely singular continuous spectrum supported on a…

We extend some recent results of Lubinsky, Levin, Simon, and Totik from measures with compact support to spectral measures of Schr\"odinger operators on the half-line. In particular, we define a reproducing kernel $S_L$ for Schr\"odinger…

We say that a discrete set $X =\{x_n\}_{n\in\dN_0}$ on the half-line $$0=x_0 < x_1 <x_2 <x_3<... <x_n<... <+\infty$$ is sparse if the distances $\Delta x_n = x_{n+1} -x_n$ between neighbouring points satisfy the condition $\frac{\Delta…

The norm resolvent convergence of a family of one-dimensional Schroedinger operators with singular magnetic and electric potentials of small support is studied.

We study the spectral properties of ergodic Schr\"{o}dinger operators that are associated to a certain family of non-primitive substitutions on a binary alphabet. The corresponding subshifts provide examples of dynamical systems that go…

We study the spectrum of a one-dimensional Schroedinger operator perturbed by a fast oscillating potential. The oscillation period is a small parameter. The essential spectrum is found in an explicit form. The existence and multiplicity of…

We consider perturbations of quasi-periodic Schr\"odinger operators on the integer lattice with analytic sampling functions by decaying potentials and seek decay conditions under which various spectral properties are preserved. In the…