{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T19:01:25Z","timestamp":1790881285682,"version":"4.1.0"},"reference-count":46,"publisher":"American Physical Society (APS)","issue":"1","license":[{"start":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T00:00:00Z","timestamp":1784851200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/W010097\/1"],"award-info":[{"award-number":["EP\/W010097\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/X025 373\/1"],"award-info":[{"award-number":["EP\/X025 373\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["101076233"],"award-info":[{"award-number":["101076233"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. E"],"accepted":{"date-parts":[[2026,6,9]]},"abstract":"<jats:p>We derive statistical distributions for the degrees of freedom in wave packet molecular dynamics models. Specifically, a theory is developed for the width distributions of Gaussian wave packets in both isotropic and anisotropic formulations. The resulting distribution functions show good agreement with molecular dynamics data under warm dense matter conditions, providing practical guidance for constraining the confining potential, an empirical parameter in the model. We also discuss how these distributions influence the resulting effective Coulomb interactions.<\/jats:p>","DOI":"10.1103\/3w8y-wj1r","type":"journal-article","created":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T16:10:27Z","timestamp":1781021427000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Statistical theory of electronic degrees of freedom in wave packet molecular dynamics"],"prefix":"10.1103","volume":"114","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-7619-0688","authenticated-orcid":true,"given":"Daniel","family":"Plummer","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/052gg0110","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Oxford"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7013-208X","authenticated-orcid":true,"given":"Pontus","family":"Svensson","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/052gg0110","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Oxford"},{"id":[{"id":"https:\/\/ror.org\/01zy2cs03","id-type":"ROR","asserted-by":"publisher"}],"name":"Helmholtz-Zentrum Dresden-Rossendorf"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wiktor","family":"Jasniak","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/052gg0110","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Oxford"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Patrick","family":"Hollebon","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02gv4h649","id-type":"ROR","asserted-by":"publisher"}],"name":"AWE"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1016-0975","authenticated-orcid":true,"given":"Sam M.","family":"Vinko","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/052gg0110","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Oxford"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4153-0628","authenticated-orcid":true,"given":"Gianluca","family":"Gregori","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/052gg0110","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Oxford"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2026,7,24]]},"reference":[{"key":"3w8y-wj1rCc1R1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6587\/ae672c","type":"journal-article"},{"key":"3w8y-wj1rCc2R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2022.09.001","type":"journal-article"},{"key":"3w8y-wj1rCc3R1","doi-asserted-by":"publisher","DOI":"10.1086\/171391","type":"journal-article"},{"key":"3w8y-wj1rCc4R1","doi-asserted-by":"publisher","DOI":"10.1126\/science.286.5437.72","type":"journal-article"},{"key":"3w8y-wj1rCc5R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.5017970","type":"journal-article"},{"key":"3w8y-wj1rCc6R1","doi-asserted-by":"publisher","DOI":"10.1063\/5.0138955","type":"journal-article"},{"key":"3w8y-wj1rCc7R1","doi-asserted-by":"publisher","DOI":"10.1063\/5.0219405","type":"journal-article"},{"key":"3w8y-wj1rCc8R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.103.013203","type":"journal-article"},{"key":"3w8y-wj1rCc9R1","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jctc.3c00934","type":"journal-article"},{"key":"3w8y-wj1rCc10R1","doi-asserted-by":"publisher","DOI":"10.1557\/s43579-022-00273-7","type":"journal-article"},{"key":"3w8y-wj1rCc11R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.70.046411","type":"journal-article"},{"key":"3w8y-wj1rCc12R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.78.025401","type":"journal-article"},{"key":"3w8y-wj1rCc13R1","doi-asserted-by":"publisher","DOI":"10.1063\/5.0298952","type":"journal-article"},{"key":"3w8y-wj1rCc14R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.72.655","type":"journal-article"},{"key":"3w8y-wj1rCc15R1","volume-title":"Frontiers and Challenges in Warm Dense Matter","author":"P.\u00a0E. Grabowski","year":"2014","type":"book"},{"key":"3w8y-wj1rCc16R1","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(94)91015-4","type":"journal-article"},{"key":"3w8y-wj1rCc17R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.76.036406","type":"journal-article"},{"key":"3w8y-wj1rCc18R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.104.045304","type":"journal-article"},{"key":"3w8y-wj1rCc19R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.110.055205","type":"journal-article"},{"key":"3w8y-wj1rCc20R1","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/42\/21\/214044","type":"journal-article"},{"key":"3w8y-wj1rCc21R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.111.045208","type":"journal-article"},{"key":"3w8y-wj1rCc22R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.2.043139","type":"journal-article"},{"key":"3w8y-wj1rCc23R1","doi-asserted-by":"publisher","DOI":"10.1063\/5.0028925","type":"journal-article"},{"key":"3w8y-wj1rCc24R1","doi-asserted-by":"publisher","DOI":"10.3390\/plasma4020020","type":"journal-article"},{"key":"3w8y-wj1rCc25R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(96)00948-6","type":"journal-article"},{"key":"3w8y-wj1rCc26R1","doi-asserted-by":"publisher","DOI":"10.1103\/x4j6-9d29","type":"journal-article"},{"key":"3w8y-wj1rCc27R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.111.015204","type":"journal-article"},{"key":"3w8y-wj1rCc28R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.122.015001","type":"journal-article"},{"key":"3w8y-wj1rCc29R1","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/39\/17\/S01","type":"journal-article"},{"key":"3w8y-wj1rCc30R1","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2022.0325","type":"journal-article"},{"key":"3w8y-wj1rCc31R1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511609633","type":"book","volume-title":"Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods","author":"D. Marx","year":"2009"},{"key":"3w8y-wj1rCc32R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.99.185003","type":"journal-article"},{"key":"3w8y-wj1rCc33R1","doi-asserted-by":"publisher","DOI":"10.1002\/ctpp.201800179","type":"journal-article"},{"key":"3w8y-wj1rCc34R1","doi-asserted-by":"publisher","DOI":"10.1002\/ctpp.201500139","type":"journal-article"},{"key":"3w8y-wj1rCc35R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.467889","type":"journal-article"},{"key":"3w8y-wj1rCc36R1","doi-asserted-by":"publisher","DOI":"10.1088\/1742-6596\/1787\/1\/012043","type":"journal-article"},{"key":"3w8y-wj1rCc37R1","volume-title":"Random Matrices","author":"M. L. Mehta","year":"2004","type":"book"},{"key":"3w8y-wj1rCc38R1","doi-asserted-by":"publisher","DOI":"10.1002\/ctpp.2150390114","type":"journal-article"},{"key":"3w8y-wj1rCc39R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1699114","type":"journal-article"},{"key":"3w8y-wj1rCc40R1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/57.1.97","type":"journal-article"},{"key":"3w8y-wj1rCc41R1","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-4145-2","type":"book","volume-title":"Monte Carlo Statistical Methods","author":"C. Robert","year":"2004"},{"key":"3w8y-wj1rCc42R1","doi-asserted-by":"crossref","DOI":"10.1201\/b16018","type":"book","volume-title":"Bayesian Data Analysis","author":"A. Gelman","year":"2013"},{"key":"3w8y-wj1rCc43R1","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1177011136","type":"journal-article"},{"key":"3w8y-wj1rCc44R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ppnp.2004.05.002","type":"journal-article"},{"key":"3w8y-wj1rCc45R1","unstructured":"D. Plummer and G. Gregori, Figure data: A statistical theory of electronic degrees of freedom in wave packet molecular dynamics, University of Oxford, ORA, 2026, https:\/\/ora.ox.ac.uk\/objects\/uuid:ba82ae3a-6af8-490f-b16c-6b341e5c875a.","type":"dataset"},{"key":"3w8y-wj1rCc46R1","volume-title":"Table of Integrals, Series, and Products","author":"I.\u00a0S. Gradshteyn","year":"2000","type":"book"}],"container-title":["Physical Review E"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/3w8y-wj1r","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/3w8y-wj1r\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T18:11:34Z","timestamp":1790878294000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/3w8y-wj1r"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,24]]},"references-count":46,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,7]]}},"URL":"https:\/\/doi.org\/10.1103\/3w8y-wj1r","relation":{"has-preprint":[{"id-type":"doi","id":"10.48550\/arXiv.2602.02088","asserted-by":"subject"}]},"ISSN":["2470-0045","2470-0053"],"issn-type":[{"value":"2470-0045","type":"print"},{"value":"2470-0053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,24]]},"assertion":[{"value":"2026-02-17","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"Published by the American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2026","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92026 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"015219"}}