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

Trabelsi, Saber; Mauser, Norbert; Bardos, Claude; Catto, Isabelle

Trabelsi, Saber; Mauser, Norbert; Bardos, Claude; Catto, Isabelle (2009), Global-in-time existence of solutions to the multiconfiguration time-dependent Hartree-Fock equations: A sufficient condition, Applied Mathematics Letters, 22, 2, p. 147-152. http://dx.doi.org/10.1016/j.aml.2007.12.033

Type

Article accepté pour publication ou publié

Date

2009

Journal name

Applied Mathematics Letters

Volume

Number

Pages

147-152

Abstract (EN)

The multiconfiguration time-dependent Hartree–Fock (MCTDHF for short) system is an approximation of the linear many-particle Schrödinger 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”.

Subjects / Keywords

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