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

共 50 条

[41] Solitary solutions for a class of Schrodinger equations in R3
Wang, Youjun
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2016, 67 (04):
[42] Hamilton operators and homothetic motions in R3
Yayli, Y
Yaz, N
Karacan, MK
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, 2004, 25 (08) : 898 - 902
[43] Spectral gaps of the Schrodinger operators with periodic δ'-interactions and Diophantine approximations
Yoshitomi, Kazushi
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2007, 143 : 185 - 199
[44] On algebraic minimal surfaces in R3 deriving from charge 2 monopole spectral curves
Small, A
INTERNATIONAL JOURNAL OF MATHEMATICS, 2005, 16 (02) : 173 - 180
[45] TRACE FORMULAS AND INVERSE SPECTRAL THEORY FOR SCHRODINGER-OPERATORS
GESZTESY, F
HOLDEN, H
SIMON, B
ZHAO, Z
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 29 (02) : 250 - 255
[46] Low energy spectral and scattering theory for relativistic Schrodinger operators
Richard, Serge
Umeda, Tomio
HOKKAIDO MATHEMATICAL JOURNAL, 2016, 45 (02) : 141 - 179
[47] SPECTRAL THEORY OF RANDOM SCHRODINGER-OPERATORS - A GENETIC INTRODUCTION
LANG, R
LECTURE NOTES IN MATHEMATICS, 1991, 1498 : U1 - &
[48] Spectral and scattering theory for Schrodinger operators on perturbed topological crystals
Parra, D.
Richard, S.
REVIEWS IN MATHEMATICAL PHYSICS, 2018, 30 (04)
[49] On spectral theory for Schrodinger operators with operator-valued potentials
Gesztesy, Fritz
Weikard, Rudi
Zinchenko, Maxim
JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 255 (07) : 1784 - 1827
[50] SPECTRAL THEORY OF MAGNETIC SCHRODINGER-OPERATORS WITH EXPLODING POTENTIALS
YAMADA, O
JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 1990, 30 (04): : 585 - 623

← 1 2 3 4 5 →