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.
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页码：1305 / 1347
页数：43
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