{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"d2a4e0a617a9e71a110d55aa8b6ab523449afac5a5741fcdf3365e514ba7ce6c","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["0dc16ba0ceacd872d5cf73607f23aa0867d4fc3bf520ec82b05ce9303ef63a0d","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"55dd7b5f6ffc7f8f88ccc99b227589834bc281b3c3f1f6aed7f2f1d583efef57","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":"2","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":"0dc16ba0ceacd872d5cf73607f23aa0867d4fc3bf520ec82b05ce9303ef63a0d","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 $\\mathrm{ErFeO_3}$ (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":null},"content_withheld":"false","files":[],"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"0643591dddd6bb634318e527b87fcaa916145865576814d0160e32ce72862c6b","schema":"pubphys.attested/1"},"id_token":null,"id_token_withheld":"false","envelope":{"attested_hash":"fdc93c30fbe6667c776d3b500ffd432bcb4cc71631115b8d8dc794deba578dc8","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"LClbh1C76IeYcvE2GKvFQjltQLzVbrAgPcFERyGEJnFuv-BmkyQ32q5FvJ6FkpyfvEsgma_Pu-2yqBbR55ObBg"},"schema":"pubphys.envelope/1"},"ots":{"attested":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEI_ck8MPvmZnx3bTtQD_1DK8tMxxYxEVuNjceU3rpXjcjxIP2nQp6xCSDlsiR64jJ0VIKQ6m5zU-cftuodW8SeOWG3CPEg0LWZERAnHChGFFMFcbl4Ur0HC8GQLRxS_dYHOxLBxfkI8CBd_s9-RqQWWrC2hch-ZguG4-zNh6B2ytSwWkmmltNFrQjxIGILGEqcRsoyMJvOgi4ObDaxfgVrN8-vytrGFeoNmxV7CPEgmdVJ5ikAbLtRlwxQnDg3EzWjB3GdCESFjFY2sALNycsI8CCx7ozj3FYE1xZoCg4D2rOc_t3B6JRkyL9SJH5THLYvxAjxIKp9_b8q9YTYpqYzV3WJr0nrK70p1RKkujfc3hP22RZICPEgLknXQLPBphDVPQ2JIPapNIpNFDYAu57cOPZiO3xVZPcI8SBFZ7nkuh-5IaK75jNF2I3u9gWIJeTINL1f_rXWP5TwxwjxIK8CKI34eu_sgR6N3zB1SKGijO7ko6-mgEUnS-DdScYBCP_wCOf1iajMfCj1CPAQnjpoz1kO_dN22pXdltGw2AjxIE4XykgsZ_WSh2vkwqZCzoJ33eOitoafeDpQ-3_6R7A_CPAg4b6CYztt395HgCIMw1-W5LfG-vu-JwtH6wIGvmq0bZwI8CCtU0WsKh5BwLGGWacTQHMeBHwdClkCV-rMMMXN9ZvwZQjxBGrRZZPwCNknZwX9zuTwAIPf4w0u-QyOLCtodHRwczovL2JvYi5idGMuY2FsZW5kYXIub3BlbnRpbWVzdGFtcHMub3Jn8Aj1kxLXPF3sgQjwEN3TRaAlnRGdywLUXJqL_hoI8SC_EwWue7sXTkhbkg2KtpDc5URgyM3Hol8HHDVDiM8uLgjxBGrRZZLwCDbPE8C0jkmw_wCD3-MNLvkMji4taHR0cHM6Ly9hbGljZS5idGMuY2FsZW5kYXIub3BlbnRpbWVzdGFtcHMub3JnCPEgcCe_goUV_i6JgQUm8vGIzFLLPxWjAk_iuhN8MP2HtsgI8CCPm2C9s0XubFI_iMYYTrp7NQVEucjiDVVOS-5XhW0I8AjwILGVzUe4o5G4eCfsNghhwOFziij306RNYES910HKmhrsCPAgVyONoXyQM0NgJkZo0hKVGO9f4juKf5A3CyvglhBsUm8I8CCeXSTiCzsu5jmLW6aIc74nszLe4FOEslRZChj0t1VKtAjxIDr4W3XX8r8aow1ZiGRWxWoIW9dJhunhLwmguwsGdTO-CPEgELz-YATskE_flI3EMFwbuOgsnBRGkzF1Xa9I7rj-MQ4I8SB7TgKiPXFKLsITxTCqIEY2E_JnlB0P9hnCf6F5J05tTgjxIGB0NKCvdVTHWPyb-krv47MzDAWBd4vLje6N98K_6F_kCPAgyX4-cC3jGOgERVTj6eTI3Q0pFr0C9fiQQx-WUXIglL0I8VkBAAAAAfPitX67BAWDTZtWcQxQWCkh0YqMzi1a4gPWRNWeuOKwAAAAAAD-____AlREAgAAAAAAFgAUEXKzahzT5T5tisLdW6UYvM0Pl9sAAAAAAAAAACJqIPAEctMOAAgI8SAwkgFiLjrE4i4UPDMn2c7HXieBbkduCVR_rk5GmSghhwgI8CAeAZYQYIMdaCxzBP3Y06gnuz57Ns-TKJavZGdhkML93AgI8CC198zLIu74yxwmwNzR3PAaynBKuua9UCcw2CyBaEcKWAgI8CAxSXU58ENTCGnlVmMfBUDSe7PUXkdlNQkIcCczUvUXcwgI8CBK0rtRametS55XkRoTu4TTLoEsynoQA2atuGtOoQFm7wgI8CDktVbsge1QvmY068_HWE5N8syaqVDu30QVb4oO2shIhAgI8CAAGBdnq6kVTyqINAoW1AWmqSMrCXQ-zEzglSNUuUMpuQgI8CATBv3oWI6GOVvAjwYVlDhrkZfDGzhtR2pU4wqu0FZXfQgI8SCoGD7CnRzwIA9X2TonvAhr38a1B-laaGkTXOoVnKLalAgI8CDalktNU8YluuKLPRSEzK1gNVgBc6BCdYNysw57Ar07xwgI8SDGbdDDNu9PiyInO5tAadJPrtta_57FjBI8_UoOLsJpTAgI8SCbq51S51-NRozSBQVPKUoYMzKmPum0xMbTObF39PnJNwgI8CAyk4ieSMUJWnWk5mF9mfI8CXyF1YaYfNBysYuAvBIouAgIAAWIlg1z1xkBA_OmOw"],"envelope":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIFiXK-fXSJUmUzUAAdPiuDveam5Akyz14T4_5Bo9MdJvwIBYyH9GUKvZDJnmE9dnNFLAzVyOHKM2jR8gAXetI8e0BCPAgaag-tYqNWNPJOEtzHSxdLMhWSSiWUAjQtil1snxoLz8I8SBu8rz_9Q6qChoTrERiLLnrB46TzZT4ee9S1QzCnNikrAjwII-WetL-ucm-WryZjOkKfskt94dacEbj-oxf9lqv55FvCPAgfpSOVZuHJJGgcmuN804B2FjKKXliyr1pSeovqOjnS90I8SCmhj8C10RPltL1Kxc5lLU861II5Y9KOZjcQg_JCQcQKgjwIBOvfBQRBP4iTAnLt1neEKzJY5cH42A1iH1qQbJbWNT7CPAgQEjWwWlWWX3vJoLxfq0lixNb2cwGMRGhB0ekxjFJDZAI8SCHI26f1bMr-H5VtXG_HgMHDd8PPImPLhsWPB8PPaY3jwjwIKD8mGRUgbk2Dt1xG-4OxMpCuw1ya5UEUQXsqASURGCtCPAgkPXX-naXR0fRIdS-sEDlzYmtMvSCNH42ESUF0QXb6NUI8CDQo_sIWZiWXaTGRSQBLmU-lHJKskYKqsjO1r02DhB8LAj_8Ajn9YmozHwo9QjwEJ46aM9ZDv3TdtqV3ZbRsNgI8SBOF8pILGf1kodr5MKmQs6Cd93joraGn3g6UPt_-kewPwjwIOG-gmM7bd_eR4AiDMNfluS3xvr7vicLR-sCBr5qtG2cCPAgrVNFrCoeQcCxhlmnE0BzHgR8HQpZAlfqzDDFzfWb8GUI8QRq0WWT8AjZJ2cF_c7k8ACD3-MNLvkMjiwraHR0cHM6Ly9ib2IuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZ_AI9ZMS1zxd7IEI8BDd00WgJZ0RncsC1Fyai_4aCPEgvxMFrnu7F05IW5INiraQ3OVEYMjNx6JfBxw1Q4jPLi4I8QRq0WWS8Ag2zxPAtI5JsP8Ag9_jDS75DI4uLWh0dHBzOi8vYWxpY2UuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZwjxIHAnv4KFFf4uiYEFJvLxiMxSyz8VowJP4roTfDD9h7bICPAgj5tgvbNF7mxSP4jGGE66ezUFRLnI4g1VTkvuV4VtCPAI8CCxlc1HuKORuHgn7DYIYcDhc4oo99OkTWBEvddBypoa7AjwIFcjjaF8kDNDYCZGaNISlRjvX-I7in-QNwsr4JYQbFJvCPAgnl0k4gs7LuY5i1umiHO-J7My3uBThLJUWQoY9LdVSrQI8SA6-Ft11_K_GqMNWYhkVsVqCFvXSYbp4S8JoLsLBnUzvgjxIBC8_mAE7JBP35SNxDBcG7joLJwURpMxdV2vSO64_jEOCPEge04Coj1xSi7CE8UwqiBGNhPyZ5QdD_YZwn-heSdObU4I8SBgdDSgr3VUx1j8m_pK7-OzMwwFgXeLy43ujffCv-hf5AjwIMl-PnAt4xjoBEVU4-nkyN0NKRa9AvX4kEMfllFyIJS9CPFZAQAAAAHz4rV-uwQFg02bVnEMUFgpIdGKjM4tWuID1kTVnrjisAAAAAAA_v___wJURAIAAAAAABYAFBFys2oc0-U-bYrC3VulGLzND5fbAAAAAAAAAAAiaiDwBHLTDgAICPEgMJIBYi46xOIuFDwzJ9nOx14ngW5HbglUf65ORpkoIYcICPAgHgGWEGCDHWgscwT92NOoJ7s-ezbPkyiWr2RnYZDC_dwICPAgtffMyyLu-MscJsDc0dzwGspwSrrmvVAnMNgsgWhHClgICPAgMUl1OfBDUwhp5VZjHwVA0nuz1F5HZTUJCHAnM1L1F3MICPAgStK7UWpnrUueV5EaE7uE0y6BLMp6EANmrbhrTqEBZu8ICPAg5LVW7IHtUL5mNOvPx1hOTfLMmqlQ7t9EFW-KDtrISIQICPAgABgXZ6upFU8qiDQKFtQFpqkjKwl0PsxM4JUjVLlDKbkICPAgEwb96FiOhjlbwI8GFZQ4a5GXwxs4bUdqVOMKrtBWV30ICPEgqBg-wp0c8CAPV9k6J7wIa9_GtQfpWmhpE1zqFZyi2pQICPAg2pZLTVPGJbriiz0UhMytYDVYAXOgQnWDcrMOewK9O8cICPEgxm3QwzbvT4siJzubQGnST67bWv-exYwSPP1KDi7CaUwICPEgm6udUudfjUaM0gUFTylKGDMypj7ptMTG0zmxd_T5yTcICPAgMpOInkjFCVp1pOZhfZnyPAl8hdWGmHzQcrGLgLwSKLgICAAFiJYNc9cZAQPzpjs"]},"log":{"leaf_index":"2204","tree_size":"3804","proof":["ec9dbdb9c6eae8dfedf34acef71afef98317e770008085bf7bd1eb9e99541d8d","fcbb84f1a6108d69a8ff5f137250482ef1da3efc75b552c0cbb9c0b513e79dde","ca96bc6ade440b342a0ee2a25d87f66036955cefa30ba8d1440149d671d0b573","bf35e744130bd10c1d2f4b241df2ef0d0af25de3044e263dbfeab08162e7cbe1","2c6dc5133c02e4efc5bc6eb6c070f0135742369909f7d9372d0be8e6d364010d","9c11194190be928ce5e60bec8c0009100dbe9ee1d681e748e41ca5a853138d17","6a6dd27141672b28efa1ee62891bc3591ef1954d1d4256adbabec756be6e0a64","9761eb0f4689d6e5f28934059787de8a9f8da3f799c91405afdf99769db5c00d","9f197ad4a050ba9a768c42080a12af180f8a85b30776c547c433648f943b3824","453fe2db8b5276d732edac85634e8be036b4709a91a2584f32a4b9edcc8ca9de","325287f5a43e4f3ad4072ec4bd53d43c50c1393021a056122e9cb0fad83b868f","3c578dccc15502c5f3efe228cadc99fee76ab536ed01f66b14d316fdcc157429"],"checkpoint":"pubphys.com/log/v1\n3804\nAK6t4qgu96+M9wScTrIlsJ10d/zhKVEtYguyM3aeJvo=\n\n— pubphys.com/log/v1 JFPwIPP8EtoxgcsQg7V7CwIdL4UKPqJtpv+eB8sFNJjyQHIdyA1VabmBsPyLqq2bLxJPn57rA6fQi8y0QDDjRXHvlQg=\n","promise":"pubphys.com/log/v1 promise\n35c7c78c3dc452e6fa0caf8f32220de7211241c07049154032fc512a55a5a571\n2204\n2026-10-15T23:43:57Z\n2026-10-16T01:43:57Z\n\n— pubphys.com/log/v1 JFPwIMz5orObtCdCVcl2QRktmNuArrH2IJcAsDMhBUgzkuAeDh0Gz1C2P8OHyP1zfQ8lrtzliH0MK9EYrnwghZenbAk=\n"},"orcid_key_evidence":[],"attesting":null}