相关论文: Half-line eigenfunction estimates and singular con…

We provide a concise, yet fairly complete discussion of the concept of essential closures of subsets of the real axis and their intimate connection with the topological support of absolutely continuous measures. As an elementary application…

We develop an algebraic approach to studying the spectral properties of the stationary Schr\"odinger equation in one dimension based on its high order conditional symmetries. This approach makes it possible to obtain in explicit form…

We characterize the absolutely continuous spectrum of the one-dimensional Schr\"odinger operators $h=-\Delta+v$ acting on $\ell^2(\mathbb{Z}_+)$ in terms of the limiting behavior of the Landauer-B\"uttiker and Thouless conductances of the…

We give a simple argument that if a quasiperiodic multi-frequency Schr\"odinger cocycle is reducible to a constant rotation for almost all energies with respect to the density of states measure, then the spectrum of the dual operator is…

The paper studies the spectral properties of the Schr\"odinger operator $A_{gV} = A_0 + gV$ on a homogeneous rooted metric tree, with a decaying real-valued potential $V$ and a coupling constant $g\ge 0$. The spectrum of the free Laplacian…

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…

We establish concrete criteria for fully supported absolutely continuous spectrum for ergodic CMV matrices and purely absolutely continuous spectrum for limit-periodic CMV matrices. We proceed by proving several variational estimates on the…

This paper aims to investigate the pseudo-modes of the one-dimensional Schr\"odinger operator with complex potentials, focusing on the behavior of the resolvent norm along specific curves in the complex plane and assessing the stability of…

We define a Schr\"odinger operator on the half-space with a discontinuous magnetic field having a piecewise-constant strength and a uniform direction. Motivated by applications in the theory of superconductivity, we study the infimum of the…

The discrete one-dimensional Schr\"odinger operator is studied in the finite interval of length $N=2 M$ with the Dirichlet boundary conditions and an arbitrary potential even with respect to the spacial reflections. It is shown, that the…

We consider Schr\"odinger operators with periodic magnetic and electric potentials on periodic discrete graphs. The spectrum of such operators consists of a finite number of bands. We determine trace formulas for the magnetic Schr\"odinger…

We prove that the spectrum of Schroedinger operators in three dimensions is purely continuous and coincides with the non-negative semiaxis for all potentials satisfying a form-subordinate smallness condition. By developing the method of…

We prove that limit-periodic Dirac operators generically have spectra of zero Lebesgue measure and that a dense set of them have spectra of zero Hausdorff dimension. The proof combines ideas of Avila from a Schr\"odinger setting with a new…

We consider the spectral problem for the two-dimensional Schr\"odinger operator for a charged particle in strong uniform magnetic and periodic electric fields. The related classical problem is analyzed first by means of the…

We present a new approach to solve a Schr\"odinger Equation autonomous at infinity, by identifying the relation between the arrangement of the spectrum of the concerned operator and the behavior of the nonlinearity at zero and at infinity.…

We consider the Schr\"odinger operator $H_{\eta W} = -\Delta + \eta W$, self-adjoint in $L^2({\mathbb R}^d)$, $d \geq 1$. Here $\eta$ is a non constant almost periodic function, while $W$ decays slowly and regularly at infinity. We study…

We establish $\frac{1}{2}$-H\"older continuity, or even the Lipschitz property, for the spectral measures of half-line discrete Schr\"odinger operators under suitable boundary conditions and exponentially decaying small potentials. These…

In this paper, we prove that for any $d$-frequency analytic quasiperiodic Schr\"odinger operator, if the frequency is weak Liouvillean, and the potential is small enough, then the corresponding operator has absolutely continuous spectrum.…

We consider the one-dimensional Stark-Wannier type operators with potentials given by a smooth function with a logarithmic growth at infinity plus a periodic function with the Fourier coefficients of the form $(\ln |n|)^{-b}, 0<b<1/2$. We…

We study two abstract scenarios, where an operator family has a certain minimality property. In both scenarios, it is shown that norm, spectrum and resolvent are the same for all family members. Both abstract settings are illustrated by…