Mean Field Limit for Bosons and Infinite Dimensional Phase-Space Analysis

被引:74
作者
Ammari, Zied [1 ]
Nier, Francis [2 ]
机构
[1] Univ Cergy Pontoise, Dept Math, CNRS, UMR 8088, F-95302 Cergy Pontoise, France
[2] Univ Rennes 1, CNRS, UMR 6625, IRMAR, F-35042 Rennes, France
来源
ANNALES HENRI POINCARE | 2008年 / 9卷 / 08期
关键词
D O I
10.1007/s00023-008-0393-5
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
This article proposes the construction of Wigner measures in the infinite dimensional bosonic quantum field theory, with applications to the derivation of the mean field dynamics. Once these asymptotic objects are well defined, it is shown how they can be used to make connections between different kinds of results or to prove new ones.
引用
收藏
页码:1503 / 1574
页数:72
相关论文
共 46 条
[11]  
Berezin F. A, 1991, MATH ITS APPL SOVIET, V66
[12]  
BONY JM, 1989, ANN SCI ECOLE NORM S, V22, P377
[13]   FUNCTIONAL SPACES ASSOCIATED WITH THE WEYL-HORMANDER CALCULUS [J].
BONY, JM ;
CHEMIN, JY .
BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 1994, 122 (01) :77-118
[14]  
BRATTELLI O, 1981, OPERATOR ALGEBRAS QU, V2
[15]  
BURQ N, 1996, SEMINAIRE BOURBAKI, V39, P29
[16]   N-boson time-dependent problem: A reformulation with stochastic wave functions [J].
Carusotto, I. ;
Castin, Y. ;
Dalibard, J. .
Physical Review A - Atomic, Molecular, and Optical Physics, 2001, 63 (02) :023606-023601
[17]  
Castin Y, 2001, LES HOUCH S, V72, P5
[18]   A proof of the Gutzwiller semiclassical trace formula using coherent states decomposition [J].
Combescure, M ;
Ralston, J ;
Robert, D .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1999, 202 (02) :463-480
[19]  
Coudene Y., 2002, GAZ MATH, P10
[20]   Spectral and scattering theory of spatially cut-off P (φ)2 Hamiltonians [J].
Derezinski, J ;
Gérard, C .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2000, 213 (01) :39-125