{"id":"https://openalex.org/W2047968614","doi":"https://doi.org/10.1103/physrev.94.262","title":"Atomic Theory of the Two-Fluid Model of Liquid Helium","display_name":"Atomic Theory of the Two-Fluid Model of Liquid Helium","publication_year":1954,"publication_date":"1954-04-15","ids":{"openalex":"https://openalex.org/W2047968614","doi":"https://doi.org/10.1103/physrev.94.262","mag":"2047968614"},"language":"en","primary_location":{"id":"doi:10.1103/physrev.94.262","doi":"https://doi.org/10.1103/physrev.94.262","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrev.94.262","pdf_url":null,"source":{"id":"https://openalex.org/S54862371","display_name":"Physical Review","issn_l":"0031-899X","issn":["0031-899X","1536-6065"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037710835","display_name":"Richard P. Feynman","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"R. P. Feynman","raw_affiliation_strings":["California Institute of Technology, Pasadena, California","California institute of Technology, Pasadena, California#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"California Institute of Technology, Pasadena, California","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"California institute of Technology, Pasadena, California#TAB#","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5037710835"],"corresponding_institution_ids":["https://openalex.org/I122411786"],"apc_list":null,"apc_paid":null,"fwci":13.4905,"has_fulltext":false,"cited_by_count":1048,"citation_normalized_percentile":{"value":0.99378367,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"94","issue":"2","first_page":"262","last_page":"277"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11965","display_name":"Quantum, superfluid, helium dynamics","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11965","display_name":"Quantum, superfluid, helium dynamics","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.0,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13645","display_name":"Thermodynamic and Structural Properties of Metals and Alloys","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/liquid-helium","display_name":"liquid helium","score":0.8939999938011169},{"id":"https://openalex.org/keywords/two-fluid-model","display_name":"two-fluid model","score":0.9869999885559082},{"id":"https://openalex.org/keywords/rotons","display_name":"rotons","score":0.6349999904632568},{"id":"https://openalex.org/keywords/excitation","display_name":"excitation","score":0.5040000081062317},{"id":"https://openalex.org/keywords/structure-factor","display_name":"structure factor","score":0.6800000071525574},{"id":"https://openalex.org/keywords/phonons","display_name":"phonons","score":0.7919999957084656},{"id":"https://openalex.org/keywords/variational-trial-functions","display_name":"variational trial functions","score":0.699999988079071},{"id":"https://openalex.org/keywords/lambda-transition","display_name":"lambda transition","score":0.5329999923706055},{"id":"https://openalex.org/keywords/critical-flow-velocity","display_name":"critical flow velocity","score":0.8140000104904175},{"id":"https://openalex.org/keywords/helium-3-in-helium-4","display_name":"helium-3 in helium-4","score":0.8939999938011169},{"id":"https://openalex.org/keywords/effective-mass","display_name":"effective mass","score":0.8989999890327454},{"id":"https://openalex.org/keywords/superfluidity","display_name":"superfluidity","score":0.5419999957084656},{"id":"https://openalex.org/keywords/hydrodynamic-equations","display_name":"hydrodynamic equations","score":0.6759999990463257}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.763694167137146},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.612724781036377},{"id":"https://openalex.org/C17816496","wikidata":"https://www.wikidata.org/wiki/Q7269050","display_name":"Quantum fluid","level":3,"score":0.4285946786403656},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4172844886779785},{"id":"https://openalex.org/C184779094","wikidata":"https://www.wikidata.org/wiki/Q26383","display_name":"Atomic physics","level":1,"score":0.4096614718437195},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3264167308807373},{"id":"https://openalex.org/C25536358","wikidata":"https://www.wikidata.org/wiki/Q106667","display_name":"Superfluidity","level":2,"score":0.2259368896484375},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1103/physrev.94.262","doi":"https://doi.org/10.1103/physrev.94.262","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrev.94.262","pdf_url":null,"source":{"id":"https://openalex.org/S54862371","display_name":"Physical Review","issn_l":"0031-899X","issn":["0031-899X","1536-6065"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review","raw_type":"journal-article"},{"id":"pmh:oai:authors.library.caltech.edu:3539","doi":null,"is_oa":false,"landing_page_url":"https://authors.library.caltech.edu/3539/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"display_name":"Affordable and clean energy","score":0.6899999976158142,"id":"https://metadata.un.org/sdg/7"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1483017919","https://openalex.org/W1525536549","https://openalex.org/W1964851430","https://openalex.org/W1988803442","https://openalex.org/W2017736011","https://openalex.org/W2033665508","https://openalex.org/W2326203395"],"related_works":["https://openalex.org/W1993313992","https://openalex.org/W2004881341","https://openalex.org/W3111248863","https://openalex.org/W1990878049","https://openalex.org/W2010516692","https://openalex.org/W2013703333","https://openalex.org/W2066483233","https://openalex.org/W2103590922","https://openalex.org/W2028805845","https://openalex.org/W2949348175"],"abstract_inverted_index":{"It":[0],"is":[1,22,28,36,61,125,170,212],"argued":[2],"that":[3],"the":[4,17,23,34,43,50,54,62,66,90,97,103,115,138,149,160,176,179,197],"wave":[5,25],"function":[6,30,48],"representing":[7],"an":[8,215],"excitation":[9],"in":[10,89,96,144,195,214],"liquid":[11,67],"helium":[12],"should":[13,199],"be":[14,218],"nearly":[15],"of":[16,31,65,123,132,159,178,185,192,206],"form":[18,110],"$\\ensuremath{\\Sigma}{i}^{}f({\\mathrm{r}}_{i})\\ensuremath{\\varphi}$,":[19],"where":[20,59],"$\\ensuremath{\\varphi}$":[21],"ground-state":[24],"function,":[26],"$f(\\mathrm{r})$":[27],"some":[29],"position,":[32],"and":[33,93,156,182],"sum":[35],"taken":[37],"over":[38],"each":[39],"atom":[40],"$i$.":[41],"In":[42],"variational":[44],"principle":[45],"this":[46,166],"trial":[47,135],"minimizes":[49],"energy":[51,55],"if":[52],"$f(\\mathrm{r})=\\mathrm{exp}(i\\mathrm{k}\\ifmmode\\cdot\\else\\textperiodcentered\\fi{}\\mathrm{r})$,":[53],"value":[56,122],"being":[57],"$E(k)=\\frac{{\\ensuremath{\\hbar}}^{2}{k}^{2}}{2mS(k)}$,":[58],"$S(k)$":[60,81],"structure":[63],"factor":[64],"for":[68],"neutron":[69],"scattering.":[70],"For":[71,78],"small":[72],"$k$,":[73,80],"$E$":[74],"rises":[75],"linearly":[76],"(phonons).":[77],"larger":[79],"has":[82],"a":[83,87,94,133,189],"maximum":[84],"which":[85,109],"makes":[86],"ring":[88],"diffraction":[91],"pattern":[92],"minimum":[95,139],"$E(k)$":[98,105],"vs":[99],"$k$":[100],"curve.":[101],"Near":[102],"minimum,":[104],"behaves":[106],"as":[107,202],"$\\ensuremath{\\Delta}+\\frac{{\\ensuremath{\\hbar}}^{2}{(k\\ensuremath{-}{k}_{0})}^{2}}{2\\ensuremath{\\mu}}$,":[108],"Landau":[111],"found":[112],"agrees":[113],"with":[114,175,183],"data":[116],"on":[117],"specific":[118],"heat.":[119],"The":[120,154,168],"theoretical":[121],"$\\ensuremath{\\Delta}$":[124],"twice":[126],"too":[127],"high,":[128],"however,":[129],"indicating":[130],"need":[131],"better":[134],"function.Excitations":[136],"near":[137],"are":[140,163],"shown":[141],"to":[142,173,217],"behave":[143],"all":[145],"essential":[146],"ways":[147],"like":[148],"rotons":[150],"postulated":[151],"by":[152],"Landau.":[153],"thermodynamic":[155],"hydrodynamic":[157],"equations":[158],"two-fluid":[161],"model":[162],"discussed":[164],"from":[165],"view.":[167],"view":[169],"not":[171],"adequate":[172],"deal":[174],"details":[177],"$\\ensuremath{\\lambda}$":[180],"transition":[181],"problems":[184],"critical":[186],"flow":[187],"velocity.In":[188],"dilute":[190],"solution":[191],"${\\mathrm{He}}^{3}$":[193,198],"atoms":[194],"${\\mathrm{He}}^{4}$,":[196],"move":[200],"essentially":[201],"free":[203],"particles":[204],"but":[205],"higher":[207],"effective":[208],"mass.":[209],"This":[210],"mass":[211,222],"calculated,":[213],"appendix,":[216],"about":[219],"six":[220],"atomic":[221],"units.":[223]},"counts_by_year":[{"year":2026,"cited_by_count":13},{"year":2025,"cited_by_count":22},{"year":2024,"cited_by_count":25},{"year":2023,"cited_by_count":15},{"year":2022,"cited_by_count":23},{"year":2021,"cited_by_count":33},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":20},{"year":2018,"cited_by_count":25},{"year":2017,"cited_by_count":31},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":18},{"year":2014,"cited_by_count":27},{"year":2013,"cited_by_count":21},{"year":2012,"cited_by_count":25}],"updated_date":"2026-10-15T10:00:46.086208","created_date":"2025-10-10T00:00:00"}
