Absolutely continuous spectrum for Schrödinger operators with random decaying matrix potentials on the strip
نویسندگان
چکیده
We consider a family of random Schrödinger operators on the discrete strip with decaying $$\ell ^2$$ matrix potential. prove that spectrum is almost surely pure absolutely continuous, apart from random, possibly embedded, eigenvalues which may accumulate at band edges.
منابع مشابه
On the Absolutely Continuous Spectrum of Multi-dimensional Schrödinger Operators with Slowly Decaying Potentials
1. In this short paper we extend the method of Laptev-Naboko-Safronov [15]. New estimates for the discrete spectrum obtained in this paper allow one to prove stronger results compared to [15]. The main technical tool of the paper [15] is the so called trace inequality, which relates properties of negative eigenvalues to the properties of the a.c. spectrum. Based on this relation, the technique ...
متن کاملAbsolutely Continuous Spectrum for One-dimensional Schr Odinger Operators with Slowly Decaying Potentials: Some Optimal Results
and some self-adjoint boundary condition at the origin. We assume that U is some bounded function for which HU has absolutely continuous spectrum. The presence of the absolutely continuous spectrum has direct consequences for the physical properties of the quantum particle described by the operator HU (see, e.g. [23, 2]). If we perturb this operator by some decaying potential V (x), the Weyl cr...
متن کاملAbsolutely Continuous Spectrum of Dirac Operators with Square Integrable Potentials
We show that the absolutely continuous part of the spectral function of the one-dimensional Dirac operator on a half-line with a constant mass term and a real, square-integrable potential is strictly increasing throughout the essential spectrum (−∞,−1] ∪ [1,∞). The proof is based on estimates for the transmission coefficient for the full-line scattering problem with a truncated potential and a ...
متن کاملOn the Preservation of Absolutely Continuous Spectrum for Schrödinger Operators
We present general principles for the preservation of a.c. spectrum under weak perturbations. The Schrödinger operators on the strip and on the Caley tree (Bethe lattice) are considered. In this paper, we consider the problem of preservation of a.c. spectrum for Schrödinger operators when the perturbation (potential) is decaying slowly at infinity. In a recent years, lots of results in this dir...
متن کاملAbsolutely Continuous Spectrum of Perturbed Stark Operators
In this paper, we study the stability of the absolutely continuous spectrum of onedimensional Stark operators under various classes of perturbations. Stark Schrödinger operators describe behavior of the charged particle in the constant electric field. The absolutely continuous spectrum is a manifestation of the fact that the particle described by the operator propagates to infinity at a rather ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Letters in Mathematical Physics
سال: 2023
ISSN: ['0377-9017', '1573-0530']
DOI: https://doi.org/10.1007/s11005-023-01632-8