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

Claude Bardos*, Isabelle Catto, Norbert J. Mauser, Saber Trabelsi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

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".

Original languageEnglish (US)
Pages (from-to)147-152
Number of pages6
JournalApplied Mathematics Letters
Volume22
Issue number2
DOIs
StatePublished - Feb 2009

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics

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