Skip navigation
Skip navigation

Uniform electron gases. I. Electrons on a ring

Loos, Pierre-François; Gill, Peter M. W.

Description

We introduce a new paradigm for one-dimensional uniform electron gases (UEGs). In this model, n electrons are confined to a ring and interact via a bare Coulomb operator. We use Rayleigh-Schrödinger perturbation theory to show that, in the high-density regime, the ground-state reduced (i.e., per electron) energy can be expanded as ε(rs,n)=ε0(n)r−2s+ε1(n)r−1s+ε2(n)+ε3(n)rs+⋯ , where r s is the Seitz radius. We use strong-coupling perturbation theory and show that, in the low-density regime, the...[Show more]

dc.contributor.authorLoos, Pierre-François
dc.contributor.authorGill, Peter M. W.
dc.date.accessioned2015-09-22T01:27:29Z
dc.date.available2015-09-22T01:27:29Z
dc.identifier.issn0021-9606
dc.identifier.urihttp://hdl.handle.net/1885/15622
dc.description.abstractWe introduce a new paradigm for one-dimensional uniform electron gases (UEGs). In this model, n electrons are confined to a ring and interact via a bare Coulomb operator. We use Rayleigh-Schrödinger perturbation theory to show that, in the high-density regime, the ground-state reduced (i.e., per electron) energy can be expanded as ε(rs,n)=ε0(n)r−2s+ε1(n)r−1s+ε2(n)+ε3(n)rs+⋯ , where r s is the Seitz radius. We use strong-coupling perturbation theory and show that, in the low-density regime, the reduced energy can be expanded as ε(rs,n)=η0(n)r−1s+η1(n)r−3/2s+η2(n)r−2s+⋯ . We report explicit expressions for ε0(n), ε1(n), ε2(n), ε3(n), η0(n), and η1(n) and derive the thermodynamic (large-n) limits of each of these. Finally, we perform numerical studies of UEGs with n = 2, 3, …, 10, using Hylleraas-type and quantum Monte Carlo methods, and combine these with the perturbative results to obtain a picture of the behavior of the new model over the full range of n and r s values.
dc.description.sponsorshipP.M.W.G. thanks the Australian Research Council (Grant Nos. DP0984806, DP1094170, and DP120104740) for funding. P.F.L. thanks the Australian Research Council for a Discovery Early Career Researcher Award (Grant No. DE130101441).
dc.publisherAmerican Institute of Physics
dc.rightshttp://www.sherpa.ac.uk/romeo/issn/1089-7690..."Publishers version/PDF may be used on author's personal website, institutional website or institutional repository" from SHERPA/RoMEO site (as at 22/09/15). Copyright 2013 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Chemical Physics and may be found at https://doi.org/10.1063/1.4802589
dc.sourceJournal of Chemical Physics
dc.subjectgases
dc.subjectmonte carlo method
dc.subjectelectrons
dc.subjectquantum theory
dc.titleUniform electron gases. I. Electrons on a ring
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume138
dcterms.dateAccepted2013-04-08
dc.date.issued2013-04-30
local.identifier.absfor030701
local.identifier.ariespublicationf5625xPUB3372
local.publisher.urlhttps://www.aip.org/
local.type.statusPublished Version
local.contributor.affiliationLoos, Pierre-Francois, College of Physical and Mathematical Sciences, CPMS Research School of Chemistry, RSC General, The Australian National University
local.contributor.affiliationGill, Peter, College of Physical and Mathematical Sciences, CPMS Research School of Chemistry, RSC General, The Australian National University
dc.relationhttp://purl.org/au-research/grants/arc/DP0984806
dc.relationhttp://purl.org/au-research/grants/arc/DP1094170
dc.relationhttp://purl.org/au-research/grants/arc/DP120104740
dc.relationhttp://purl.org/au-research/grants/arc/DE130101441
local.identifier.essn1089-7690
local.bibliographicCitation.issue16
local.bibliographicCitation.startpage164124
local.bibliographicCitation.lastpage9
local.identifier.doi10.1063/1.4802589
local.identifier.absseo970103
dc.date.updated2015-12-11T08:04:01Z
local.identifier.scopusID2-s2.0-84877265903
local.identifier.thomsonID000318550800028
CollectionsANU Research Publications

Download

File Description SizeFormat Image
01_Loos_Uniform_electron_gases._I._2013.pdfPublished Version2.72 MBAdobe PDFThumbnail


Items in Open Research are protected by copyright, with all rights reserved, unless otherwise indicated.

Updated:  19 May 2020/ Responsible Officer:  University Librarian/ Page Contact:  Library Systems & Web Coordinator