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

dc.contributor.authorHajaiej, Hichem
dc.contributor.authorMarkowich, Peter A.
dc.contributor.authorTrabelsi, Saber
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.institutionDepartment of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
dc.date.accessioned2015-08-03T11:47:54Z
dc.date.available2015-08-03T11:47:54Z
dc.date.issued2013-12-29
dc.date.published-online2013-12-29
dc.date.published-print2014-03
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.
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.
dc.identifier.citationHAJAIEJ, H., MARKOWICH, P. A., & TRABELSI, S. (2013). MULTICONFIGURATION HARTREE–FOCK THEORY FOR PSEUDORELATIVISTIC SYSTEMS: THE TIME-DEPENDENT CASE. Mathematical Models and Methods in Applied Sciences, 24(03), 599–626. doi:10.1142/s0218202513500619
dc.identifier.doi10.1142/S0218202513500619
dc.identifier.issn02182025
dc.identifier.journalMathematical Models and Methods in Applied Sciences
dc.identifier.urihttp://hdl.handle.net/10754/563411
dc.publisherWorld Scientific Pub Co Pte Lt
dc.subjectCauchy problem
dc.subjectdensity matrix
dc.subjectHartree
dc.subjectHartree-Fock
dc.subjectmulticonfiguration
dc.subjectsemi-relativistic
dc.subjectWell-posedness
dc.titleMulticonfiguration hartree-fock theory for pseudorelativistic systems: The time-dependent case
dc.typeArticle
display.details.left<span><h5>Type</h5>Article<br><br><h5>Authors</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Hajaiej, Hichem,equals">Hajaiej, Hichem</a><br><a href="https://repository.kaust.edu.sa/search?query=orcid.id:0000-0002-3704-1821&spc.sf=dc.date.issued&spc.sd=DESC">Markowich, Peter A.</a> <a href="https://orcid.org/0000-0002-3704-1821" target="_blank"><img src="https://repository.kaust.edu.sa/server/api/core/bitstreams/82a625b4-ed4b-40c8-865a-d6a5225a26a4/content" width="16" height="16"/></a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Trabelsi, Saber,equals">Trabelsi, Saber</a><br><br><h5>KAUST Department</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Applied Mathematics and Computational Science Program,equals">Applied Mathematics and Computational Science Program</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division,equals">Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division</a><br><br><h5>Online Publication Date</h5>2013-12-29<br><br><h5>Print Publication Date</h5>2014-03<br><br><h5>Date</h5>2013-12-29</span>
display.details.right<span><h5>Abstract</h5>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.<br><br><h5>Citation</h5>HAJAIEJ, H., MARKOWICH, P. A., & TRABELSI, S. (2013). MULTICONFIGURATION HARTREE–FOCK THEORY FOR PSEUDORELATIVISTIC SYSTEMS: THE TIME-DEPENDENT CASE. Mathematical Models and Methods in Applied Sciences, 24(03), 599–626. doi:10.1142/s0218202513500619<br><br><h5>Acknowledgements</h5>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.<br><br><h5>Publisher</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.publisher=World Scientific Pub Co Pte Lt,equals">World Scientific Pub Co Pte Lt</a><br><br><h5>Journal</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.journal=Mathematical Models and Methods in Applied Sciences,equals">Mathematical Models and Methods in Applied Sciences</a><br><br><h5>DOI</h5><a href="https://doi.org/10.1142/S0218202513500619">10.1142/S0218202513500619</a></span>
kaust.personMarkowich, Peter A.
kaust.personTrabelsi, Saber
orcid.authorHajaiej, Hichem
orcid.authorMarkowich, Peter A.::0000-0002-3704-1821
orcid.authorTrabelsi, Saber
orcid.id0000-0002-3704-1821
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