The Gell-Mann–Brueckner Formula for the Correlation Energy of the Electron Gas: A Rigorous Upper Bound in the Mean-Field Regime
We prove a rigorous upper bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of interaction potentials. Our result covers the Coulomb potential, and in this case we obtain the analogue of the Gell-Mann–Brueckner formula c 1 ρ log ρ + c 2 ρ in the high d...
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| Veröffentlicht in: | Communications in mathematical physics 2023-07, Vol.401 (2), p.1469-1529 |
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| container_end_page | 1529 |
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| container_issue | 2 |
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| container_title | Communications in mathematical physics |
| container_volume | 401 |
| creator | Christiansen, Martin Ravn Hainzl, Christian Nam, Phan Thành |
| description | We prove a rigorous upper bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of interaction potentials. Our result covers the Coulomb potential, and in this case we obtain the analogue of the Gell-Mann–Brueckner formula
c
1
ρ
log
ρ
+
c
2
ρ
in the high density limit. We do this by refining the analysis of our bosonization method to deal with singular potentials, and to capture the exchange contribution which is absent in the purely bosonic picture. |
| doi_str_mv | 10.1007/s00220-023-04672-2 |
| format | Article |
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c
1
ρ
log
ρ
+
c
2
ρ
in the high density limit. We do this by refining the analysis of our bosonization method to deal with singular potentials, and to capture the exchange contribution which is absent in the purely bosonic picture.</description><identifier>ISSN: 0010-3616</identifier><identifier>EISSN: 1432-0916</identifier><identifier>DOI: 10.1007/s00220-023-04672-2</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Classical and Quantum Gravitation ; Complex Systems ; Coulomb potential ; Electron gas ; Fermions ; Mathematical and Computational Physics ; Mathematical Physics ; Physics ; Physics and Astronomy ; Quantum Physics ; Relativity Theory ; Theoretical ; Upper bounds</subject><ispartof>Communications in mathematical physics, 2023-07, Vol.401 (2), p.1469-1529</ispartof><rights>The Author(s) 2023</rights><rights>The Author(s) 2023. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c363t-2074532f1b51d4700569cc0f4135d53352cd952f9c4e41908718a7adb7160a3a3</citedby><cites>FETCH-LOGICAL-c363t-2074532f1b51d4700569cc0f4135d53352cd952f9c4e41908718a7adb7160a3a3</cites><orcidid>0000-0002-9772-7323</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00220-023-04672-2$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00220-023-04672-2$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Christiansen, Martin Ravn</creatorcontrib><creatorcontrib>Hainzl, Christian</creatorcontrib><creatorcontrib>Nam, Phan Thành</creatorcontrib><title>The Gell-Mann–Brueckner Formula for the Correlation Energy of the Electron Gas: A Rigorous Upper Bound in the Mean-Field Regime</title><title>Communications in mathematical physics</title><addtitle>Commun. Math. Phys</addtitle><description>We prove a rigorous upper bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of interaction potentials. Our result covers the Coulomb potential, and in this case we obtain the analogue of the Gell-Mann–Brueckner formula
c
1
ρ
log
ρ
+
c
2
ρ
in the high density limit. We do this by refining the analysis of our bosonization method to deal with singular potentials, and to capture the exchange contribution which is absent in the purely bosonic picture.</description><subject>Classical and Quantum Gravitation</subject><subject>Complex Systems</subject><subject>Coulomb potential</subject><subject>Electron gas</subject><subject>Fermions</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Theoretical</subject><subject>Upper bounds</subject><issn>0010-3616</issn><issn>1432-0916</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kEFOwzAQRS0EEqVwAVaWWBvGduIk7ErVFqRWSFW7ttzECSmpXexk0R2cgRtyEkyDxI7VSDPv_5EeQtcUbilAcucBGAMCjBOIRMIIO0EDGnFGIKPiFA0AKBAuqDhHF95vASBjQgzQx-pF45luGrJQxny9fz64TuevRjs8tW7XNQqX1uE2UGPrnG5UW1uDJwGoDtiWx8uk0Xnrwnqm_D0e4WVdWWc7j9f7fSh6sJ0pcG2O7EIrQ6a1bgq81FW905forFSN11e_c4jW08lq_Ejmz7On8WhOci54SxgkUcxZSTcxLaIEIBZZnkMZUR4XMecxy4ssZmWWRzqiGaQJTVWiik1CBSiu-BDd9L17Z9867Vu5tZ0z4aVkKacpJHF4MESsp3JnvXe6lHtX75Q7SAryR7XsVcugWh5VSxZCvA_5AJtKu7_qf1LfTMCAdQ</recordid><startdate>20230701</startdate><enddate>20230701</enddate><creator>Christiansen, Martin Ravn</creator><creator>Hainzl, Christian</creator><creator>Nam, Phan Thành</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-9772-7323</orcidid></search><sort><creationdate>20230701</creationdate><title>The Gell-Mann–Brueckner Formula for the Correlation Energy of the Electron Gas: A Rigorous Upper Bound in the Mean-Field Regime</title><author>Christiansen, Martin Ravn ; Hainzl, Christian ; Nam, Phan Thành</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c363t-2074532f1b51d4700569cc0f4135d53352cd952f9c4e41908718a7adb7160a3a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Classical and Quantum Gravitation</topic><topic>Complex Systems</topic><topic>Coulomb potential</topic><topic>Electron gas</topic><topic>Fermions</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Physics</topic><topic>Relativity Theory</topic><topic>Theoretical</topic><topic>Upper bounds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Christiansen, Martin Ravn</creatorcontrib><creatorcontrib>Hainzl, Christian</creatorcontrib><creatorcontrib>Nam, Phan Thành</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Communications in mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Christiansen, Martin Ravn</au><au>Hainzl, Christian</au><au>Nam, Phan Thành</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Gell-Mann–Brueckner Formula for the Correlation Energy of the Electron Gas: A Rigorous Upper Bound in the Mean-Field Regime</atitle><jtitle>Communications in mathematical physics</jtitle><stitle>Commun. Math. Phys</stitle><date>2023-07-01</date><risdate>2023</risdate><volume>401</volume><issue>2</issue><spage>1469</spage><epage>1529</epage><pages>1469-1529</pages><issn>0010-3616</issn><eissn>1432-0916</eissn><abstract>We prove a rigorous upper bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of interaction potentials. Our result covers the Coulomb potential, and in this case we obtain the analogue of the Gell-Mann–Brueckner formula
c
1
ρ
log
ρ
+
c
2
ρ
in the high density limit. We do this by refining the analysis of our bosonization method to deal with singular potentials, and to capture the exchange contribution which is absent in the purely bosonic picture.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00220-023-04672-2</doi><tpages>61</tpages><orcidid>https://orcid.org/0000-0002-9772-7323</orcidid><oa>free_for_read</oa></addata></record> |
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| language | eng |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Classical and Quantum Gravitation Complex Systems Coulomb potential Electron gas Fermions Mathematical and Computational Physics Mathematical Physics Physics Physics and Astronomy Quantum Physics Relativity Theory Theoretical Upper bounds |
| title | The Gell-Mann–Brueckner Formula for the Correlation Energy of the Electron Gas: A Rigorous Upper Bound in the Mean-Field Regime |
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