Spectral Asymptotics for Schrödinger Operators with Periodic Point Interactions

نویسندگان
چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Spectral Asymptotics for Schrödinger Operators with Periodic Point Interactions

Spectrum of the second-order differential operator with periodic point interactions in L2 R is investigated. Classes of unitary equivalent operators of this type are described. Spectral asymptotics for the whole family of periodic operators are calculated. It is proven that the first several terms in the asymptotics determine the class of equivalent operators uniquely. It is proven that the spe...

متن کامل

Periodic 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 کامل

Nonclassical Eigenvalue Asymptotics for Operators of Schrödinger

which depends on the volume u)n of the unit sphere in R n and the beta function. Assuming /3 < 2 we see that integral (2) becomes divergent if V (x) vanishes to a sufficiently high order. The simplest such potential is V(x,y) = \x\\y\P o n R n + R m . The Weyl (volume counting) principle, when applied to the corresponding Schrödinger operator — A-hV(x), fails to predict discrete spectrum below ...

متن کامل

Schrödinger Operators with Fairly Arbitrary Spectral Features

It is shown, using methods of inverse-spectral theory, that there exist Schrödinger operators on the line with fairly general spectral features. Thus, for instance, it follows from the main theorem, that if 0 < α < 1 is arbitrary, and if Σ is any perfect subset of (−∞, 0] with Hausdorff dimension α, then there exist potentials q j , j = 1, 2 such that the associated Schrödinger operators H j ar...

متن کامل

Spectral Asymptotics for Dirichlet Elliptic Operators with Non-smooth Coefficients

We consider a 2m-th-order elliptic operator of divergence form in a domain  of Rn, assuming that the coefficients are Hölder continuous of exponent r 2 (0, 1]. For the self-adjoint operator associated with the Dirichlet boundary condition we improve the asymptotic formula of the spectral function e( 2m , x , y) for x = y to obtain the remainder estimate O( n + dist(x , ) 1 n 1) with any 2 (0,...

متن کامل

ذخیره 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 Analysis and Applications

سال: 2002

ISSN: 0022-247X

DOI: 10.1006/jmaa.2001.7716