Spectral Theory for Schrodinger Operators with δ-Interactions Supported on Curves in R3

被引：0

作者：

Behrndt, Jussi ^{[1
]}

Frank, Rupert L. ^{[2
]}

Kuehn, Christian ^{[1
]}

Lotoreichik, Vladimir ^{[3
]}

Rohleder, Jonathan ^{[4
]}

机构：

[1] Graz Univ Technol, Inst Numer Mathemat, Steyrergasse 30, A-8010 Graz, Austria

[2] CALTECH, Math 253 37, Pasadena, CA 91125 USA

[3] Czech Acad Sci, Dept Theoret Phys, Inst Nucl Phys, Rez 25068, Czech Republic

[4] TU Hamburg, Inst Math, Schwarzenberg Campus 3,Gebaude E, D-21073 Hamburg, Germany

来源：

ANNALES HENRI POINCARE | 2017年 / 18卷 / 04期

基金：

奥地利科学基金会;

关键词：

BOUNDARY-VALUE-PROBLEMS; SELF-ADJOINT OPERATORS; SINGULAR PERTURBATIONS; ABSOLUTE CONTINUITY; HAMILTONIANS; INEQUALITIES;

D O I：

10.1007/s00023-016-0532-3

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The main objective of this paper is to systematically develop a spectral and scattering theory for self-adjoint Schrodinger operators with delta-interactions supported on closed curves in R-3. We provide bounds for the number of negative eigenvalues depending on the geometry of the curve, prove an isoperimetric inequality for the principal eigenvalue, derive Schatten-von Neumann properties for the resolvent difference with the free Laplacian, and establish an explicit representation for the scattering matrix.

引用

页码：1305 / 1347

页数：43

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