Negative discrete spectrum of perturbed multivortex Aharonov-Bohm Hamiltonians

被引：27
作者：
Melgaard, M [1 ]
Ouhabaz, EM
Rozenblum, G
机构：
[1] Uppsala Univ, Dept Math, S-75106 Uppsala, Sweden
[2] Univ Bordeaux 1, Lab Bordelais Anal & Geometrie, F-33405 Talence, France
[3] Chalmers Univ Technol, Dept Math, S-41296 Gothenburg, Sweden
[4] Univ Gothenburg, S-41296 Gothenburg, Sweden
来源：
ANNALES HENRI POINCARE | 2004年 / 5卷 / 05期
关键词：
D O I：
10.1007/s00023-004-0187-3
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
The diamagnetic inequality is established for the Schrodinger operator H-0((d)) in L-2 (R-d), d=2, 3, describing a particle moving in a magnetic field generated by finitely or infinitely many Aharonov-Bohm solenoids located at the points of a discrete set in R-2, e.g., a lattice. This fact is used to prove the Lieb-Thirring inequality as well as CLR-type eigenvalue estimates for the perturbed Schrodinger operator H-0((d))-V, using new Hardy type inequalities. Large coupling constant eigenvalue asymptotic formulas for the perturbed operators are also proved.
引用
收藏
页码：979 / 1012
页数：34
相关论文
共 35 条
  • [1] The mesostructure - properties linkage in polycrystals
    Adams, BL
    Olson, T
    [J]. PROGRESS IN MATERIALS SCIENCE, 1998, 43 (01) : 1 - 87
  • [2] [Anonymous], 1998, ST PETERSBG MATH J
  • [3] SCHRODINGER OPERATORS WITH MAGNETIC-FIELDS .1. GENERAL INTERACTIONS
    AVRON, J
    HERBST, I
    SIMON, B
    [J]. DUKE MATHEMATICAL JOURNAL, 1978, 45 (04) : 847 - 883
  • [4] On the number of negative eigenvalues of Schrodinger operators with an Aharonov-Bohm magnetic field
    Balinsky, AA
    Evans, WD
    Lewis, RT
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2001, 457 (2014): : 2481 - 2489
  • [5] Balinsky AA, 2003, MATH RES LETT, V10, P169
  • [6] WEAK LOCALIZATION IN A DISTRIBUTION OF MAGNETIC-FLUX TUBES
    BENDING, SJ
    VONKLITZING, K
    PLOOG, K
    [J]. PHYSICAL REVIEW LETTERS, 1990, 65 (08) : 1060 - 1063
  • [7] Birman M.S., 1991, ADV SOVIET MATH, V7
  • [8] Birman M. Sh., 1990, OPER THEORY ADV APPL, V46, P3
  • [9] BIRMAN M. SH., 1970, FUNCT ANAL APPL+, V4, P1
  • [10] The negative discrete spectrum of the operator (-Delta)(l)-alpha V in L-2(R-d) for d even and 2l>=d
    Birman, MS
    Laptev, A
    Solomyak, M
    [J]. ARKIV FOR MATEMATIK, 1997, 35 (01): : 87 - 126
1234