THE SEMICLASSICAL LIMIT OF THE TIME DEPENDENT HARTREE-FOCK EQUATION: THE WEYL SYMBOL OF THE SOLUTION

被引：22
|
作者：
Amour, Laurent [1 ]
Khodja, Mohamed [1 ]
Nourrigat, Jean [1 ]
机构：
[1] Univ Reims, Lab Math Reims, FR CNRS 3399, EA 4535, F-51687 Reims, France
来源：
ANALYSIS & PDE | 2013年 / 6卷 / 07期
关键词：
time dependent Hartree-Fock equation; Vlasov equation; semiclassical analysis; Egorov theorem; pseudodifferential operators; MEAN-FIELD LIMIT; DYNAMICS; SYSTEMS;
D O I：
10.2140/apde.2013.6.1649
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For a family of solutions to the time dependent Hartree-Fock equation, depending on the semiclassical parameter h, we prove that if at the initial time the Weyl symbol of the solution is in L-1(R-2n) as well as all its derivatives, then this property is true for all time, and we give an asymptotic expansion in powers of h of this Weyl symbol. The main term of the asymptotic expansion is a solution to the Vlasov equation, and the error term is estimated in the norm of L-1(R-2n).
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页码：1649 / 1674
页数：26
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