{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"e17fbb265dba07876ae1796cfd1fa3cba720350293c64ac0a898ded1ee060743","created":"2026-10-03T07:17:53Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"088ce4fa33f26485a1d39c11fcd8457ef8645bded766969ad3c9458180a17411","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"amo.cavity-photon-matter.equilibrium-superradiance","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"Simple models predict that enough atoms in a cavity will spontaneously fill it with light in their lowest energy state. General theorems forbid this, yet loopholes have been proposed.","posed_since":"1975","precise":"$N$ atoms or electrons coupled to a cavity field with full minimal coupling, including the $A^{2}$ term, in thermal equilibrium. Determine whether the ground state can have $\\langle a\\rangle/\\sqrt{N} \\ne 0$ in the thermodynamic limit, given no-go theorems for uniform fields (Rzazewski et al. 1975; Andolina et al. 2019). Answer: yes for a specific realizable setting, or a general no-go proof covering spatially varying and magnetic couplings.","problem_ref":null,"references":"","settled_by":"A proof covering all gauge-invariant multimode couplings, or a model and experiment showing an equilibrium photon condensate.","status_note":"No-go theorems hold for uniform fields; photon condensation is permitted for spatially varying fields as a magnetostatic instability (Andolina et al., PRB 2020); an equilibrium magnonic analog was reported in ErFeO3 (Kim et al., Science Advances 2025), while a photonic equilibrium superradiant phase is unobserved.","title":"Does an equilibrium superradiant phase transition exist in cavity QED?","topic_ref":"8df59b7655cdc4331866853909e22dff07fb2d661e37f2a43fdc664ddd9f7dda"},"content_withheld":"false","files":[],"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"0dc16ba0ceacd872d5cf73607f23aa0867d4fc3bf520ec82b05ce9303ef63a0d","schema":"pubphys.attested/1"},"id_token":null,"id_token_withheld":"false","envelope":{"attested_hash":"e660adad8f55014b2d7418994edb0e3b2a417843351950438baf2c3938f07b17","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"qrmkuzBTOEh61CwrhmELok2I9DNWlRc9Y5051r7HIrbdk5MpImMQxZPiEjTHnYngGsVwuXm0Q-a2GMgNntzSCA"},"schema":"pubphys.envelope/1"},"ots":{"attested":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEI5mCtrY9VAUstdBiZTtsOOypBeEM1GVBDi68sOTjwexfxIOZVjbm891OeGbUIWJjLh6T6xweUTUPeCjA_0Aa2ekP3CPAgNBgWhgLRN8BdxL7CiWQfD21MsgRKaEwy4uElgkV_ke0I8SBrSH5wNDzBnh-EIHekY5R8HOjbPW57t0zlpRVLoYzn1QjwIDUORt2CorxT77xNhOLW9Bz30OqsuK8zL9dkQgfzZ3ySCPEg0wFb7eMvfeSLzbXSAMCm0SJOI6UyZl7ku7Lc2eRb77kI8SB21m8GRTmJSZYi_Lrh-hqAsLoQJTYqpgwfMrugPU1y2gjxILxzQWMAmvaultZlg8E3OUpGfSrLm6L_gGXyaZDMO7ZVCPEgX1ct-J5utS2Y9i_MQF8whgQqggfdpWZjb4EXThxsbjcI8CCoahAZNQNYu2Y_acHP7f8i7DMCAPi7QeYPsDQmFOUZcgjxIOUdEg6sSGuGAwm6byKNwNSH-CaFtay_ppzVi8InqIsBCPEgUZCxxJx-baWw4JFRfzCCtSjPn4ATBx_3FQi1O2Yo4-8I8SAQuuTPkAGyvS_wKMy9BtKvnki2puESdY2vXem8hT1uIQjwIBGYo5Vxy-d7U5zKv5vp3Ii7hJPH_BDLCzA13c47p9q7CP_wCHbghVgOFMuNCPAQPZK2lHbTMqcCYUotzOQcmQjwIJ7ruRIs6HnufKxCpmLUgeUl0aUu0ov4_3PqcppS-bddCPEgI530vHzdwz_3o9jYQ3WablSaV64Wfn7Pmby5WLyI-A0I8QRqwKw78AhITF7Tr3a1xP8Ag9_jDS75DI4sK2h0dHBzOi8vYm9iLmJ0Yy5jYWxlbmRhci5vcGVudGltZXN0YW1wcy5vcmcI8CBXWeNiWFWltfHE0nkDXsVKIykUUwuObhsnN-2fvBt98gjwIM5Vf7j68sOFgVysYMc5S09Hho-fqxYW3oQ4oKUX7JpPCPAgaKHHQB3sdd9w1hu4NMh7vmb-p0X2r4uyVKKCj1G7S28I8SAW2Mg6Bzi9ygjrrjIYB7w90fwMcxH24SsqLmzPyAMGfwjwIMQ863zlveYIpNKWVrZaDOa4vowwoOg2CcTW8gXtxK3dCPEgrZxGGAf-t8jhz_eLMUyBN1IhNrdYDRcNHWvQcwNG9woI8CCVOUHG1YXudbaFIgUYvrCIevRWvb2ubhQAo-z0duD0rQjxIDBeKerVGkO3J2eXDwdraSioXbIWsdIPEN1s8pIwJIS2CPAgV2kB3n3JZ5HwBQjpRL1CWKnqvdCjZk3RcALk6N2wHigI8CB-wbljNlfqElD25uZkNg6taS81YDRU2vfMqGVQ420O9AjxWQEAAAABJM43UU6MLMRrPlCUqossvu1q_knons5yylyWTgxZzWUAAAAAAP7___8CLgABAAAAAAAWABQrYt3E7OllKRCEmL3FL589l78_5wAAAAAAAAAAImog8ATiyw4ACAjxILmbcIO7ixv3pCtwUMZ1VQGKus54F9lZ8-w5ECD5ZuiICAjwIG6ynCyFTLPE7Rgk-0ZGCtBDyqNQx8YvaSZNHy8D8p8jCAjwIMX8zoD2Be1YWvcx_bexVPRmBX0hK-do8b8t9SarimQVCAjxIG6XtpqIEclLlhzcK1LVjqoPGrjjmLnyno8tcETMzECECAjwIF6mlfXOFY51JhrK4eze8zQlKV75OYZYqbtyi8BWxmAsCAjwIKKUcJmVoz-u-geiRV_-ZHdF0VEPXaEPFWf_JX_0e7G2CAjxIGMeD0Z5QWNKBcAEpHht007FFIILW6aSJ8f3CMkKNsneCAjwIBFr6Je8rkB7kwhPGbq0yRgFwZsvW9JhY5sXDRtrq0QwCAjwIAHAwXaus-yUgKICJB5mVvx8VZuJgjwnpb0qWPg1pi6DCAjxIAJhb8cefkVHTAMymdsxa-_i-tUua62LcpALQnPG7R9_CAjwIDvsFqBhPfAL6TCtXZd7gBWmMpx6iiZ-Ug0Jf_LlcstgCAjwIDJRBX6Q0Vge-ra-k1_g76yJWTEp6WWF13I3JpTnsZPJCAjwILykZCbkC9VQgl5gytPKKir6T9nTvKR6y05iWSHBTQgzCAgABYiWDXPXGQED45c78Ah-sGbmQAwfZwjwEAYqxtHnZiPZnJEGPx_JvKsI8SDXkqDg17YsZIrEz5acRx7mBXCKW5mKNgRYnw_-U2cpDgjxBGrArDrwCEfK6Mono428_wCD3-MNLvkMji4taHR0cHM6Ly9hbGljZS5idGMuY2FsZW5kYXIub3BlbnRpbWVzdGFtcHMub3JnCPAg10nyJ6Jn4kshQQQCKE0Lvj3hBC6nLRBVIzaPV4eh8VwI8CCQaAqWlxEbac_XOq1MOlf9iOKHEsxXspzbjK0vLpy8BwjwII3iRbRXUcDxrhAdkZmFlI15nySCSEZ7g922tF1Xln5DCPEgYYvZ1L4v4rPu_UqLfcHPtwSb2OH2GhPgVcVhhH6DpkQI8CDZCIoR20sC-uchP40oAmcLm9EJFV7xzwplj54AeVadXQjxILvLBjPFpCoz29m9Yf2qRnV7PI9GqxE8ozVQfk9QwCqrCPEgZXcMudvEoB_MJ8tqOW2PLTKAIeQBnE-1bfzptRc2gR8I8VkBAAAAAfXq-bmxWqOz7B5wKkwjzHGv2R4s7Y0Z76LqXWYNhmz0AAAAAAD-____Av0cAAAAAAAAFgAUl-skmdZDtn7Hnub6mF4HP2uVn7oAAAAAAAAAACJqIPAE4MsOAAgI8CBDmQsbEXc46Hu8DivhCBM1LGExa4TTM-wo7HpoCVjBTQgI8CCty5vkQtPHzzs8xqArOYhVSjgaDoG1ou3cojv5_P7wQQgI8SDQWB0kdXCTwbk-TqTt0QfRMyzDNLOtU1XXFgvGSRlW8wgI8CC2PKa_QCIBZtrXodq1GdEzppISMsMRDOnzr2gFjLKOAAgI8CCwQ_QF67bcFk_uJ2s0VCZmf5PGIjTmTCpt_qnVY5p_8AgI8SAbzyx7z-oxPMju6PvtQhzrJIQyH2ZAc9oyLuYemzbmZQgI8CC5bh7J74uUk91r8LwybHQFCNBC3PWeuwtMCCNFKWj19AgI8SAf4R2TUNPjaX_PWDUImpoITK0JoW89zaMKnD1wlEEi8AgI8SC2vNmdm7eyP5Ytl1yTzT0njliMdALl1ViKG-s3bG2zswgI8CCpbIVNz1GFVXdJk2zd82hBUoNFFemUPBt7IJdWEOciPwgI8CBtYdRQcrtX1FtCm1SxF7sx-5cO04U8KzbJh8fqBkyReAgI8CBHs2LGmX6gI-lV7yp1RrV7_tGfdiBAwnEFF6B6yXHzAQgI8CATotVmbXBMAixhZ-QKy5Q4lR0FusdA_wcIC1TbB7GmxAgIAAWIlg1z1xkBA-KXOw"],"envelope":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIkMaAOexMbZYdNNq21Flj5qm7nrDYJT9eMebm2CGT-S_xIJCob_TTHcN0Wg_Fbmt-Qzg3Ny4q7TS8XNbwlDEsv1zvCPAgVfI8_IbbYzD5r43ztmadJiobmKhMYxLjw4HX7iXRsJUI8SCiLQzQ16SoqOFBtMqXcDB6CI_5fm2dbdb1wKKpv9LIwwjwIFM-Jd-kjjwqBWzt-D5ozn4J0NiQtJNeeBgMjMB44aN4CPAgDbDJ5Jts0H26jCr8Dm8LRiW741ad1MNEiQmoGQHS6EwI8CAEwc_TDAArJnS7L12hyepqNpIfWdUKeTwknlQYdJa64wjxID4GM9LaCJsrZhWbEPtHBfDrOPGQi4CH8Bu_7M-4ow1RCPAgyYYKAjmHpniaTNWfQfwaMNMI3Vm3FjqZ7JUny3t_J48I8SAzYkfrMCtnlPZF7RCs0vhySIZDq30HHv5Q-Y2E93F_lgjwIIhzmnVeFxVHRiBmi7SsQd_gIBRvsrzzZf-fzyEkp8wnCPAgy6DmLQtIuWm-zrDRmaSy95vcFWsjvWyppQO7wIWrfC4I8SAQuuTPkAGyvS_wKMy9BtKvnki2puESdY2vXem8hT1uIQjwIBGYo5Vxy-d7U5zKv5vp3Ii7hJPH_BDLCzA13c47p9q7CP_wCHbghVgOFMuNCPAQPZK2lHbTMqcCYUotzOQcmQjwIJ7ruRIs6HnufKxCpmLUgeUl0aUu0ov4_3PqcppS-bddCPEgI530vHzdwz_3o9jYQ3WablSaV64Wfn7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