{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"64bf2808f715911f80e409959fe9c830aa46923277baf3bac94570dc62cd0de3","created":"2026-10-03T07:18:06Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"94928650203c28cbe21848928d797097f50c482a1771cf00498e2afc3e946ad6","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"mathph.fermi-liquids-bcs.bcs-odlro","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"BCS theory explains superconductivity by electron pairing, but it is an approximation. No one has proven that a full many-electron model with attraction actually forms a pair condensate in an infinite system.","posed_since":"","precise":"$N$ spin-$1/2$ fermions in a box of side $L$ with attractive short-range pair potential, density fixed, $L \\to \\infty$. Prove that the two-body reduced density matrix has an eigenvalue of order $N$ (Yang's off-diagonal long-range order) for $T$ below a $T_{c} > 0$, and compare $T_{c}$ with the BCS functional prediction. Answer: a proof.","problem_ref":null,"references":"","settled_by":"A proof of pair condensation in the thermodynamic limit for the full many-body Hamiltonian.","status_note":"Rigorous results concern the BCS functional (Hainzl, Hamza, Seiringer and Solovej, 2008, and later) and mean-field type Hamiltonians, not the full many-body problem.","title":"Off-diagonal long-range order in a many-body model of attractive fermions","topic_ref":"092ec16641325783d3e30e41c35811e9c4984811735d26f9a5dda60705ccb883"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"922e865ada3fa9a10a4c4bbd8bdad44622b8f2dc6e5c3d2a55c51c200fb0a144","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"705b7c2cad15d91e36e08d800bb01b2cff0c1abdc94da580f5266c945377adf9","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"fIgf7AJxSAm3Zerq5JqthSTY-Iw5LkdVDFa1F7rc_WPVXyb75uoMmZXnKoIGYpb0yzQYzvhidkiWepFYuU2UDQ"},"schema":"pubphys.envelope/1"},"record_hash":"922e865ada3fa9a10a4c4bbd8bdad44622b8f2dc6e5c3d2a55c51c200fb0a144","leaf_index":1612}