Related papers: Schr\"odinger operators with measure-valued potent…

We generalize the approach to localization in one dimension introduced by Kunz-Souillard, and refined by Delyon-Kunz-Souillard and Simon, in the early 1980's in such a way that certain correlations are allowed. Several applications of this…

We construct 1-dim difference Schr\"odinger operators with a class of Gevrey potentials such that Cantor spectrum occurs together with the estimations of open spectral gaps . The proof is based on KAM and Moser-P\"oschel argument .

This paper sets out to study the spectral minimum for operator belonging to the family of random Schr\"{o}dinger operators of the form $H\_{\lambda,\omega}=-\Delta+W\_{\text{per}}+\lambda V\_{\omega}$, where we suppose that $V\_{\omega}$ is…

We consider the discrete Schr\"odinger operator $H=-\Delta+V$ with a sparse potential $V$ and find conditions guaranteeing either existence of wave operators for the pair $H$ and $H_0=-\Delta$, or presence of dense purely point spectrum of…

We prove Strichartz estimates for the Schroedinger operator $H = -\Delta + V(t,x)$ with time-periodic complex potentials $V$ belonging to the scaling-critical space $L^{n/2}_x L^\infty_t$ in dimensions $n \ge 3$. This is done directly from…

Let $L$ be a linear, closed, densely defined in a Hilbert space operator, not necessarily selfadjoint. Consider the corresponding wave equations &(1) \quad \ddot{w}+ Lw=0, \quad w(0)=0,\quad \dot{w}(0)=f, \quad \dot{w}=\frac{dw}{dt}, \quad…

The purpose of this article is to study pseudospectral properties of the one-dimensional Schr\"{o}dinger operator perturbed by a complex steplike potential. By constructing the resolvent kernel, we show that the pseudospectrum of this…

In this article we give an overview on some recent development of Littlewood-Paley theory for Schr\"odinger operators. We extend the Littlewood-Paley theory for special potentials considered in the authors' previous work. We elaborate our…

In this paper, we develop a systematic framework to study the dispersion surfaces of Schr{\"o}dinger operators $ -\Delta + V$, where the potential $V \in C^\infty(\mathbb{R}^n,\mathbb{R})$ is periodic with respect to a lattice $\Lambda…

Schr\"odinger operator on half-line with complex potential and the corresponding evolution are studied within perturbation theoretic approach. The total number of eigenvalues and spectral singularities is effectively evaluated. Wave…

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 study the Schr\"{o}dinger operators on a non-compact star graph with the Coulomb-type potentials having singularities at the vertex. The convergence of regularized Hamiltonians $H_\varepsilon$ with cut-off Coulomb potentials coupled with…

We construct examples of potentials $V(x)$ satisfying $|V(x)| \leq \frac{h(x)}{1+x},$ where the function $h(x)$ is growing arbitrarily slowly, such that the corresponding Schr\"odinger operator has imbedded singular continuous spectrum.…

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…

This study is devoted to the asymptotic spectral analysis of multiscale Schr\"odinger operators with oscillating and decaying electric potentials. Different regimes, related to scaling considerations, are distinguished. By means of a normal…

In this paper we study the spectrum of self-adjoint Schr\"odinger operators in $L^2(\mathbb{R}^2)$ with a new type of transmission conditions along a smooth closed curve $\Sigma\subseteq \mathbb{R}^2$. Although these $\textit{oblique}$…

We study one-dimensional Schr\"odinger operators with complex measures as potentials and present an improved criterion for absence of eigenvalues which involves a weak local periodicity condition. The criterion leads to sharp quantitative…

We study continuum Schr\"odinger operators on the real line whose potentials are comprised of two compactly supported square-integrable functions concatenated according to an element of the Fibonacci substitution subshift over two letters.…

This paper investigates the $L^p$-boundedness of wave operators associated with the nonhomogeneous fourth-order Sch\"odinger operator $H = \Delta^2 - \Delta + V(x)$ on $\mathbb{R}^n$. Assuming the real-valued potential $ V $ exhibits…

We consider discrete one-dimensional Schr\"odinger operators whose potentials are generated by H\"older continuous sampling along the orbits of a uniformly hyperbolic transformation. For any ergodic measure satisfying a suitable bounded…