Coulomb Systems on Riemannian Manifolds and Stability of Matter

被引:5
作者
Enciso, Alberto [1 ]
机构
[1] CSIC, CSIC UAM UCM UC3M, Inst Ciencias Matemat, Madrid 28049, Spain
来源
ANNALES HENRI POINCARE | 2011年 / 12卷 / 04期
关键词
LIOUVILLE-TYPE THEOREM; SCHRODINGER-OPERATORS; THERMODYNAMIC LIMIT; SPECTRUM; EIGENVALUES; POTENTIALS; EQUATION; KERNEL; ATOMS;
D O I
10.1007/s00023-011-0084-5
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We analyze the spectrum of many-body Coulomb Hamiltonians in the setting of open Riemannian manifolds, proving stability of matter in any complete noncompact Riemannian three-manifold of nonnegative Ricci curvature and Euclidean volume growth.
引用
收藏
页码:723 / 741
页数:19
相关论文
共 40 条
[1]   INEQUALITIES FOR POTENTIALS OF PARTICLE-SYSTEMS [J].
BAXTER, JR .
ILLINOIS JOURNAL OF MATHEMATICS, 1980, 24 (04) :645-652
[2]  
Chung Kai Lai, 1980, Annales de l'institut Fourier, V30, P167
[3]   Large scale behavior of kernels of Schrodinger operators [J].
Colding, TH ;
Minicozzi, WP .
AMERICAN JOURNAL OF MATHEMATICS, 1997, 119 (06) :1355-1398
[4]  
DONNELLY H, 1981, MICH MATH J, V28, P53
[5]  
Donnelly H, 1997, INDIANA U MATH J, V46, P505
[6]   PURE POINT SPECTRUM AND NEGATIVE CURVATURE FOR NONCOMPACT MANIFOLDS [J].
DONNELLY, H ;
LI, P .
DUKE MATHEMATICAL JOURNAL, 1979, 46 (03) :497-503
[7]  
Donnelly H., 1997, J GEOM ANAL, V7, P241
[8]   SPECTRAL-ANALYSIS OF 2ND-ORDER ELLIPTIC-OPERATORS ON NONCOMPACT MANIFOLDS [J].
FROESE, R ;
HISLOP, P .
DUKE MATHEMATICAL JOURNAL, 1989, 58 (01) :103-129
[9]   The thermodynamic limit of quantum Coulomb systems Part II. Applications [J].
Hainzl, Christian ;
Lewin, Mathieu ;
Solovej, Jan Philip .
ADVANCES IN MATHEMATICS, 2009, 221 (02) :488-546
[10]   The thermodynamic limit of quantum Coulomb systems Part I. General theory [J].
Hainzl, Christian ;
Lewin, Mathieu ;
Solovej, Jan Philip .
ADVANCES IN MATHEMATICS, 2009, 221 (02) :454-487