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

doi:10.1016/j.aml.2007.12.033

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 journal › Article › peer-review

12 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 language	English (US)
Pages (from-to)	147-152
Number of pages	6
Journal	Applied Mathematics Letters
Volume	22
Issue number	2
DOIs	https://doi.org/10.1016/j.aml.2007.12.033
State	Published - Feb 2009
Externally published	Yes

Bibliographical note

Funding Information:
This work was supported by the Austrian Ministry of Science via its grant for the WPI, by the Austrian Science Foundation (FWF) via the Wissenschaftkolleg “Differential equations” (W17) and the START Project (Y-137-TEC), by the WWTF (Viennese Science Fund, project MA-45), as well as by the EU funded Marie Curie project DEASE (contract MEST-CT-2005-021122).

Keywords

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

ASJC Scopus subject areas

Applied Mathematics

Access to Document

10.1016/j.aml.2007.12.033

Cite this

@article{c8c2dc6c53a24133a6a598caba0082e5,

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

abstract = "The multiconfiguration time-dependent Hartree-Fock (MCTDHF for short) system is an approximation of the linear many-particle Schr{\"o}dinger 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{"}.",

keywords = "Few-electron systems, Ground State, Linear N-particle Schr{\"o}dinger equation, MCTDHF system",

author = "Claude Bardos and Isabelle Catto and Mauser, {Norbert J.} and Saber Trabelsi",

note = "Funding Information: This work was supported by the Austrian Ministry of Science via its grant for the WPI, by the Austrian Science Foundation (FWF) via the Wissenschaftkolleg “Differential equations” (W17) and the START Project (Y-137-TEC), by the WWTF (Viennese Science Fund, project MA-45), as well as by the EU funded Marie Curie project DEASE (contract MEST-CT-2005-021122).",

year = "2009",

month = feb,

doi = "10.1016/j.aml.2007.12.033",

language = "English (US)",

volume = "22",

pages = "147--152",

journal = "Applied Mathematics Letters",

issn = "0893-9659",

publisher = "Elsevier Limited",

number = "2",

}

TY - JOUR

T1 - Global-in-time existence of solutions to the multiconfiguration time-dependent Hartree-Fock equations

T2 - A sufficient condition

AU - Bardos, Claude

AU - Catto, Isabelle

AU - Mauser, Norbert J.

AU - Trabelsi, Saber

N1 - Funding Information: This work was supported by the Austrian Ministry of Science via its grant for the WPI, by the Austrian Science Foundation (FWF) via the Wissenschaftkolleg “Differential equations” (W17) and the START Project (Y-137-TEC), by the WWTF (Viennese Science Fund, project MA-45), as well as by the EU funded Marie Curie project DEASE (contract MEST-CT-2005-021122).

PY - 2009/2

Y1 - 2009/2

N2 - 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".

AB - 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".

KW - Few-electron systems

KW - Ground State

KW - Linear N-particle Schrödinger equation

KW - MCTDHF system

UR - http://www.scopus.com/inward/record.url?scp=56949099702&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2007.12.033

DO - 10.1016/j.aml.2007.12.033

M3 - Article

AN - SCOPUS:56949099702

SN - 0893-9659

VL - 22

SP - 147

EP - 152

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 2

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this