Topics on Fermi varieties of discrete periodic Schrödinger operators
نویسندگان
چکیده
This is a survey of recent progress on the irreducibility Fermi varieties, rigidity results and embedded eigenvalue problems discrete periodic Schr\"odinger operators.
منابع مشابه
Internal Lifshitz tails for discrete Schrödinger operators
We consider random Schrödinger operatorsHω acting on l2(Zd). We adapt the technique of the periodic approximations used in (2003) for the present model to prove that the integrated density of states of Hω has a Lifshitz behavior at the edges of internal spectral gaps if and only if the integrated density of states of a well-chosen periodic operator is nondegenerate at the same edges. A possible...
متن کاملSchrödinger Operators with Local Interactions on a Discrete Set
Spectral properties of 1-D Schrödinger operators HX,α := − d 2 dx2 + ∑ xn∈X αnδ(x − xn) with local point interactions on a discrete set X = {xn}n=1 are well studied when d∗ := infn,k∈N |xn − xk| > 0. Our paper is devoted to the case d∗ = 0. We consider HX,α in the framework of extension theory of symmetric operators by applying the technique of boundary triplets and the corresponding Weyl funct...
متن کاملPeriodic Schrödinger Operators with Local Defects and Spectral Pollution
This article deals with the numerical calculation of eigenvalues of perturbed periodic Schrödinger operators located in spectral gaps. Such operators are encountered in the modeling of the electronic structure of crystals with local defects, and of photonic crystals. The usual finite element Galerkin approximation is known to give rise to spectral pollution. In this article, we give a precise d...
متن کاملPeriodic waves of a discrete higher order nonlinear Schrödinger equation ∗
The Hirota equation is a higher order extension of the nonlinear Schrödinger equation by incorporating third order dispersion and one form of self steepening effect. New periodic waves for the discrete Hirota equation are given in terms of elliptic functions. The continuum limit converges to the analogous result for the continuous Hirota equation, while the long wave limit of these discrete per...
متن کاملInvariant Varieties of Periodic Points for the Discrete Euler Top
The Kowalevski workshop on mathematical methods of regular dynamics was organized by Professor Vadim Kuznetsov in April 2000 at the University of Leeds [1]. In his introductory talk about the Kowalevski top, Professor Kuznetzov [2] had shown his strong interest on the subject and motivated the authors to work on classical tops. In our recent paper [3] we have studied the behaviour of periodic p...
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: Journal of Mathematical Physics
سال: 2022
ISSN: ['0022-2488', '1527-2427', '1089-7658']
DOI: https://doi.org/10.1063/5.0078287