{ "profile": "wrs-published-research-view-1", "edition": "ratings-e039106f30dec177", "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS", "entry": { "id": "lee-huang-yang-dilute-hard-sphere-bose-calculation-1957", "title": "Lee–Huang–Yang: dilute hard-sphere Bose energy, excitations and correlations", "summary": "Lee, Huang and Yang used a pseudopotential calculation to connect the wave functions, excitations, condensate depletion and pair correlations of a dilute hard-sphere Bose gas. The 1957 paper recovers the beyond-mean-field energy correction, explicitly crediting its earlier Lee–Yang derivation, and calculates low-lying collective excitations at the stated order. Its value is the linked microscopic calculation, not a claim that every density regime of liquid helium has been solved.", "boundary": "A dilute-gas, low-temperature physical expansion for the hard-sphere model, not a rigorous all-density many-body theorem or a quantitative solution of strongly interacting liquid helium. The paper uses hbar=1 and 2 m=1, periodic boundary conditions, and a hard-sphere diameter a that equals the scattering length in this model. Small sqrt(rho a^3) and additionally ka<<1 for the excitation approximation are essential. Higher collisions and systematic higher orders remain difficulties, and convergence of the full expansion is not proved. Its discussion of nonuniform superfluid flow is explicitly suggestive rather than mathematically conclusive; existing two-fluid reasoning and Bogoliubov/Bijl/Feynman results remain inherited. The printed Eq. (52) has an inverse-square-root factor inconsistent with Eq. (31) and Eqs. (50)–(51); the excitation claim follows Eq. (31). This textual discrepancy is not silently turned into a verified published erratum.", "area": "Quantum many-body theory; dilute Bose gases", "topic": "Physics", "year": 1957, "lane": "HUMAN", "result": "THEORY", "package_id": "lee-huang-yang-dilute-hard-sphere-bose-calculation-1957", "target": { "record_id": "urn:uuid:b3c306db-6200-41ca-a5e2-5b4b7c52b784", "version": 1, "content_hash": "sha256:c8a7980db216de5e63d648b9aabe1ae87f1f730dcdca28602c70a71c74e72f07" }, "humans": [ "T. D. Lee", "Kerson Huang", "C. N. Yang" ], "authors_complete": true, "human_role_note": "Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.", "agents": [], "related": [], "subresults": [], "scientific_assessment": { "source_review": "SOURCE_CURATED", "scientific_review": "NOT_REVIEWED_BY_WRS", "formal_replay": "NOT_RUN", "provider_attestation": "NONE" }, "sources": [ { "id": "cur20261022-lhy-hard-sphere-1957", "title": "Eigenvalues and Eigenfunctions of a Bose System of Hard Spheres and Its Low-Temperature Properties (1957 original facsimile)", "url": "https://wucj.lab.westlake.edu.cn/teach/CNYang/lee1957.pdf", "date": "1957-06-15" } ], "geography": { "country_codes": [ "US" ], "location_basis": "T. D. Lee: Columbia University, New York; Kerson Huang and C. N. Yang: Institute for Advanced Study, Princeton, New Jersey, on the original first page. 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The 1957 paper recovers the beyond-mean-field energy correction, explicitly crediting its earlier Lee–Yang derivation, and calculates low-lying collective excitations at the stated order. Its value is the linked microscopic calculation, not a claim that every density regime of liquid helium has been solved.", "scope": "Lee, Huang and Yang used a pseudopotential calculation to connect the wave functions, excitations, condensate depletion and pair correlations of a dilute hard-sphere Bose gas. The 1957 paper recovers the beyond-mean-field energy correction, explicitly crediting its earlier Lee–Yang derivation, and calculates low-lying collective excitations at the stated order. Its value is the linked microscopic calculation, not a claim that every density regime of liquid helium has been solved. A dilute-gas, low-temperature physical expansion for the hard-sphere model, not a rigorous all-density many-body theorem or a quantitative solution of strongly interacting liquid helium. The paper uses hbar=1 and 2 m=1, periodic boundary conditions, and a hard-sphere diameter a that equals the scattering length in this model. Small sqrt(rho a^3) and additionally ka<<1 for the excitation approximation are essential. Higher collisions and systematic higher orders remain difficulties, and convergence of the full expansion is not proved. Its discussion of nonuniform superfluid flow is explicitly suggestive rather than mathematically conclusive; existing two-fluid reasoning and Bogoliubov/Bijl/Feynman results remain inherited. The printed Eq. (52) has an inverse-square-root factor inconsistent with Eq. (31) and Eqs. (50)–(51); the excitation claim follows Eq. (31). This textual discrepancy is not silently turned into a verified published erratum.", "status": "PROVISIONAL_EDITORIAL", "scientific_correctness_certified": false }, "assessment_disposition": { "status": "ASSESSED", "label": "Provisionally assessed", "reason": "A current grade and separate reference score identify this exact contribution.", "target": { "record_id": "urn:uuid:b3c306db-6200-41ca-a5e2-5b4b7c52b784", "version": 1, "content_hash": "sha256:c8a7980db216de5e63d648b9aabe1ae87f1f730dcdca28602c70a71c74e72f07" }, "edition": "ratings-e039106f30dec177" } }, "version": { "kind": "PUBLIC_RECORD_VIEW", "previous": null, "published_at": "2026-10-23T00:00:00Z", "publisher": { "principal_id": "urn:uuid:80116931-785b-40a2-a24b-9d59db0c7e33", "role": "WRS_EDITORIAL_PUBLICATION" }, "record": { "contributors": [ { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "T. D. Lee", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formulator" ], "source": { "citation": "Eigenvalues and Eigenfunctions of a Bose System of Hard Spheres and Its Low-Temperature Properties (1957 original facsimile)", "url": "https://wucj.lab.westlake.edu.cn/teach/CNYang/lee1957.pdf" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "Kerson Huang", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formulator" ], "source": { "citation": "Eigenvalues and Eigenfunctions of a Bose System of Hard Spheres and Its Low-Temperature Properties (1957 original facsimile)", "url": "https://wucj.lab.westlake.edu.cn/teach/CNYang/lee1957.pdf" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "C. N. Yang", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formulator" ], "source": { "citation": "Eigenvalues and Eigenfunctions of a Bose System of Hard Spheres and Its Low-Temperature Properties (1957 original facsimile)", "url": "https://wucj.lab.westlake.edu.cn/teach/CNYang/lee1957.pdf" } } ], "evidence": [ { "description": "Bibliographic/stated-result source; not a WRS proof verification", "id": "source-0", "kind": "source_reference", "source": { "citation": "Eigenvalues and Eigenfunctions of a Bose System of Hard Spheres and Its Low-Temperature Properties (1957 original facsimile)", "url": "https://wucj.lab.westlake.edu.cn/teach/CNYang/lee1957.pdf" } } ], "origin": "HUMAN_LEGACY", "record_profile": "wrs-local-research-notes-0.1", "record_type": "research_note", "rrp_version": "0.1", "scope": { "description": "A dilute-gas, low-temperature physical expansion for the hard-sphere model, not a rigorous all-density many-body theorem or a quantitative solution of strongly interacting liquid helium. The paper uses hbar=1 and 2 m=1, periodic boundary conditions, and a hard-sphere diameter a that equals the scattering length in this model. Small sqrt(rho a^3) and additionally ka<<1 for the excitation approximation are essential. Higher collisions and systematic higher orders remain difficulties, and convergence of the full expansion is not proved. Its discussion of nonuniform superfluid flow is explicitly suggestive rather than mathematically conclusive; existing two-fluid reasoning and Bogoliubov/Bijl/Feynman results remain inherited. The printed Eq. (52) has an inverse-square-root factor inconsistent with Eq. (31) and Eqs. (50)–(51); the excitation claim follows Eq. (31). This textual discrepancy is not silently turned into a verified published erratum.", "domain": "Quantum many-body theory; dilute Bose gases" }, "sources": [ { "citation": "Eigenvalues and Eigenfunctions of a Bose System of Hard Spheres and Its Low-Temperature Properties (1957 original facsimile)", "url": "https://wucj.lab.westlake.edu.cn/teach/CNYang/lee1957.pdf" } ], "statement": "# Lee–Huang–Yang: dilute hard-sphere Bose energy, excitations and correlations\n\nLee, Huang and Yang used a pseudopotential calculation to connect the wave functions, excitations, condensate depletion and pair correlations of a dilute hard-sphere Bose gas. The 1957 paper recovers the beyond-mean-field energy correction, explicitly crediting its earlier Lee–Yang derivation, and calculates low-lying collective excitations at the stated order. Its value is the linked microscopic calculation, not a claim that every density regime of liquid helium has been solved.\n\n## Scientific scope\n\nA dilute-gas, low-temperature physical expansion for the hard-sphere model, not a rigorous all-density many-body theorem or a quantitative solution of strongly interacting liquid helium. The paper uses hbar=1 and 2 m=1, periodic boundary conditions, and a hard-sphere diameter a that equals the scattering length in this model. Small sqrt(rho a^3) and additionally ka<<1 for the excitation approximation are essential. Higher collisions and systematic higher orders remain difficulties, and convergence of the full expansion is not proved. Its discussion of nonuniform superfluid flow is explicitly suggestive rather than mathematically conclusive; existing two-fluid reasoning and Bogoliubov/Bijl/Feynman results remain inherited. The printed Eq. (52) has an inverse-square-root factor inconsistent with Eq. (31) and Eqs. (50)–(51); the excitation claim follows Eq. (31). This textual discrepancy is not silently turned into a verified published erratum.\n\n## Reading status\n\nThis is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.\n\n## People and systems\n\nT. D. Lee; Kerson Huang; C. N. Yang\n\nSource-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.\n\n\n\n## Original sources\n\n- [Eigenvalues and Eigenfunctions of a Bose System of Hard Spheres and Its Low-Temperature Properties (1957 original facsimile)](https://wucj.lab.westlake.edu.cn/teach/CNYang/lee1957.pdf)\n", "summary": "Lee, Huang and Yang used a pseudopotential calculation to connect the wave functions, excitations, condensate depletion and pair correlations of a dilute hard-sphere Bose gas. The 1957 paper recovers the beyond-mean-field energy correction, explicitly crediting its earlier Lee–Yang derivation, and calculates low-lying collective excitations at the stated order. Its value is the linked microscopic calculation, not a claim that every density regime of liquid helium has been solved.", "title": "Lee–Huang–Yang: dilute hard-sphere Bose energy, excitations and correlations" }, "record_id": "urn:uuid:b3c306db-6200-41ca-a5e2-5b4b7c52b784", "version": 1, "source_ref": { "record_id": "urn:uuid:b3c306db-6200-41ca-a5e2-5b4b7c52b784", "version": 1, "content_hash": "sha256:c8a7980db216de5e63d648b9aabe1ae87f1f730dcdca28602c70a71c74e72f07" }, "export_view": "wrs-public-editorial-view-1", "public_view_hash": "sha256:795135e9bc9c14645b53ccb97b57faf87164d85511e1c8b498d9cbf84b20b147" }, "target": { "record_id": "urn:uuid:b3c306db-6200-41ca-a5e2-5b4b7c52b784", "version": 1, "content_hash": "sha256:c8a7980db216de5e63d648b9aabe1ae87f1f730dcdca28602c70a71c74e72f07" }, "published_grade": { "profile": "wrs-published-grade-1", "edition": "2026-10-28.1", "id": "lee-huang-yang-dilute-hard-sphere-bose-calculation-1957", "entry_id": "lee-huang-yang-dilute-hard-sphere-bose-calculation-1957", "revision": 1, "title": "Lee–Huang–Yang: dilute hard-sphere Bose energy, excitations and correlations", "context": "Quantum many-body theory; dilute Bose gases", "track": "Reusable scientific method, experimental result or historical framework", "band": "S", "modifier": "-", "status": "PROVISIONAL_EDITORIAL", "assessed_on": "2026-10-23", "evidence_cutoff": "2026-10-23", "achievement_state": "SUPPORTED_SCOPED_RESULT", "what_changed": "Lee, Huang and Yang used a pseudopotential calculation to connect the wave functions, excitations, condensate depletion and pair correlations of a dilute hard-sphere Bose gas. The 1957 paper recovers the beyond-mean-field energy correction, explicitly crediting its earlier Lee–Yang derivation, and calculates low-lying collective excitations at the stated order. Its value is the linked microscopic calculation, not a claim that every density regime of liquid helium has been solved.", "scope": "Lee, Huang and Yang used a pseudopotential calculation to connect the wave functions, excitations, condensate depletion and pair correlations of a dilute hard-sphere Bose gas. The 1957 paper recovers the beyond-mean-field energy correction, explicitly crediting its earlier Lee–Yang derivation, and calculates low-lying collective excitations at the stated order. Its value is the linked microscopic calculation, not a claim that every density regime of liquid helium has been solved. A dilute-gas, low-temperature physical expansion for the hard-sphere model, not a rigorous all-density many-body theorem or a quantitative solution of strongly interacting liquid helium. The paper uses hbar=1 and 2 m=1, periodic boundary conditions, and a hard-sphere diameter a that equals the scattering length in this model. Small sqrt(rho a^3) and additionally ka<<1 for the excitation approximation are essential. Higher collisions and systematic higher orders remain difficulties, and convergence of the full expansion is not proved. Its discussion of nonuniform superfluid flow is explicitly suggestive rather than mathematically conclusive; existing two-fluid reasoning and Bogoliubov/Bijl/Feynman results remain inherited. The printed Eq. (52) has an inverse-square-root factor inconsistent with Eq. (31) and Eqs. (50)–(51); the excitation claim follows Eq. (31). This textual discrepancy is not silently turned into a verified published erratum.", "evidence_summary": "The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. A dilute-gas, low-temperature physical expansion for the hard-sphere model, not a rigorous all-density many-body theorem or a quantitative solution of strongly interacting liquid helium. The paper uses hbar=1 and 2 m=1, periodic boundary conditions, and a hard-sphere diameter a that equals the scattering length in this model. Small sqrt(rho a^3) and additionally ka<<1 for the excitation approximation are essential. Higher collisions and systematic higher orders remain difficulties, and convergence of the full expansion is not proved. Its discussion of nonuniform superfluid flow is explicitly suggestive rather than mathematically conclusive; existing two-fluid reasoning and Bogoliubov/Bijl/Feynman results remain inherited. The printed Eq. (52) has an inverse-square-root factor inconsistent with Eq. (31) and Eqs. (50)–(51); the excitation claim follows Eq. (31). This textual discrepancy is not silently turned into a verified published erratum.", "references": [ { "title": "Eigenvalues and Eigenfunctions of a Bose System of Hard Spheres and Its Low-Temperature Properties (1957 original facsimile)", "url": "https://wucj.lab.westlake.edu.cn/teach/CNYang/lee1957.pdf", "locator": "Original scoped contribution, statement/method and evidence limits; source-specific attribution retained." } ], "roles": [ { "who": "The named authors in the research record", "credit": "SCIENCE", "did": "Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. 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