Global-in-time existence of solutions to the multiconfiguration time-dependent Hartree-Fock equations: A sufficient condition

被引：12

作者：

Bardos, Claude ^{[1
,2
]}

Catto, Isabelle ^{[3
]}

Mauser, Norbert J. ^{[4
]}

Trabelsi, Saber ^{[1
]}

机构：

[1] Univ Paris 07, Lab JL Lions, F-75221 Paris 05, France

[2] WPI Wien, Vienna, Austria

[3] Univ Paris 09, CNRS, UMR 7534, Ceremade, F-75775 Paris 16, France

[4] Univ Vienna, Fak F Math, Wolfgang Pauli Inst, A-1090 Vienna, Austria

来源：

APPLIED MATHEMATICS LETTERS | 2009年 / 22卷 / 02期

关键词：

MCTDHF system; Linear N-particle Schrodinger equation; Few-electron systems; Ground State; ATOMS;

D O I：

10.1016/j.aml.2007.12.033

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The multiconfiguration time-dependent Hartree-Fock (MCTDHF for short) system is an approximation of the linear many-particle Schrodinger equation with a binary interaction potential by nonlinear "one-particle" equations. MCTDHF methods are widely used for numerical calculations of the dynamics of few-electron systems in quantum physics and quantum chemistry, but the time-dependent case still poses serious open problems for the analysis, e.g. in the sense that global-in-time existence of solutions is not proved yet. In this letter we present the first result ever where global existence is proved under a condition on the initial datum that it has to be somewhat close to the "ground state". (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：147 / 152

页数：6

共 11 条

[1] Mean field dynamics of fermions and the time-dependent Hartree-Fock equation [J].

Bardos, C ;

Golse, F ;

Gottlieb, AD ;

Mauser, NJ .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2003, 82 (06) :665-683

[2]

Bardos C., 2000, Methods Appl. Anal., V7, P275

[3] Correlated multielectron systems in strong laser fields: A multiconfiguration time-dependent Hartree-Fock approach [J].

Caillat, J ;

Zanghellini, J ;

Kitzler, M ;

Koch, O ;

Kreuzer, W ;

Scrinzi, A .

PHYSICAL REVIEW A, 2005, 71 (01)

[4]

CATTO I, LOCAL WELL POS UNPUB

[5] The multiconfiguration equations for atoms and molecules: Charge quantization and existence of solutions [J].

Friesecke, G .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2003, 169 (01) :35-71

[6] On the infinitude of non-zero eigenvalues of the single-electron density matrix for atoms and molecules [J].

Friesecke, G .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2003, 459 (2029) :47-52

[7]

LEBRIS C, 1994, ANN I H POINCARE-AN, V11, P441

[8] Solutions of the multiconfiguration equations in quantum chemistry [J].

Lewin, M .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2004, 171 (01) :83-114

[9] QUANTUM THEORY OF MANY-PARTICLE SYSTEMS .1. PHYSICAL INTERPRETATIONS BY MEANS OF DENSITY MATRICES, NATURAL SPIN-ORBITALS, AND CONVERGENCE PROBLEMS IN THE METHOD OF CONFIGURATIONAL INTERACTION [J].

LOWDIN, PO .

PHYSICAL REVIEW, 1955, 97 (06) :1474-1489

[10]

LUBICH C, 2007, M2AN, V41, P315

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