Multiconfiguration hartree-fock theory for pseudorelativistic systems: The time-dependent case

Handle URI:
http://hdl.handle.net/10754/563411
Title:
Multiconfiguration hartree-fock theory for pseudorelativistic systems: The time-dependent case
Authors:
Hajaiej, Hichem; Markowich, Peter A. ( 0000-0002-3704-1821 ) ; Trabelsi, Saber
Abstract:
In [Setting and analysis of the multi-configuration time-dependent Hartree-Fock equations, Arch. Ration. Mech. Anal. 198 (2010) 273-330] the third author has studied in collaboration with Bardos, Catto and Mauser the nonrelativistic multiconfiguration time-dependent Hartree-Fock system of equations arising in the modeling of molecular dynamics. In this paper, we extend the previous work to the case of pseudorelativistic atoms. We show the existence and the uniqueness of global-in-time solution to the underlying system under technical assumptions on the energy of the initial data and the charge of the nucleus. Moreover, we prove that the result can be extended to the case of neutron stars when the number of electrons is less than a critical number N cr. © 2014 World Scientific Publishing Company.
KAUST Department:
Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
World Scientific Pub Co Pte Lt
Journal:
Mathematical Models and Methods in Applied Sciences
Issue Date:
Mar-2014
DOI:
10.1142/S0218202513500619
Type:
Article
ISSN:
02182025
Sponsors:
The authors would like to thank warmly the anonymous referees for their careful reading and criticism of the original manuscript which led to several changes and improvements. H. H. extends his appreciation to the Deanship of Scientific Research at King Saud University for funding the work through the research group project No. RGP-VPP-124.
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorHajaiej, Hichemen
dc.contributor.authorMarkowich, Peter A.en
dc.contributor.authorTrabelsi, Saberen
dc.date.accessioned2015-08-03T11:47:54Zen
dc.date.available2015-08-03T11:47:54Zen
dc.date.issued2014-03en
dc.identifier.issn02182025en
dc.identifier.doi10.1142/S0218202513500619en
dc.identifier.urihttp://hdl.handle.net/10754/563411en
dc.description.abstractIn [Setting and analysis of the multi-configuration time-dependent Hartree-Fock equations, Arch. Ration. Mech. Anal. 198 (2010) 273-330] the third author has studied in collaboration with Bardos, Catto and Mauser the nonrelativistic multiconfiguration time-dependent Hartree-Fock system of equations arising in the modeling of molecular dynamics. In this paper, we extend the previous work to the case of pseudorelativistic atoms. We show the existence and the uniqueness of global-in-time solution to the underlying system under technical assumptions on the energy of the initial data and the charge of the nucleus. Moreover, we prove that the result can be extended to the case of neutron stars when the number of electrons is less than a critical number N cr. © 2014 World Scientific Publishing Company.en
dc.description.sponsorshipThe authors would like to thank warmly the anonymous referees for their careful reading and criticism of the original manuscript which led to several changes and improvements. H. H. extends his appreciation to the Deanship of Scientific Research at King Saud University for funding the work through the research group project No. RGP-VPP-124.en
dc.publisherWorld Scientific Pub Co Pte Lten
dc.subjectCauchy problemen
dc.subjectdensity matrixen
dc.subjectHartreeen
dc.subjectHartree-Focken
dc.subjectmulticonfigurationen
dc.subjectsemi-relativisticen
dc.subjectWell-posednessen
dc.titleMulticonfiguration hartree-fock theory for pseudorelativistic systems: The time-dependent caseen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalMathematical Models and Methods in Applied Sciencesen
dc.contributor.institutionDepartment of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabiaen
kaust.authorMarkowich, Peter A.en
kaust.authorTrabelsi, Saberen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.