{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"706b1d349b725ccf19816d269a46842977ae971341f669a3820cfd7003036834","created":"2026-10-03T07:17:54Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"098141e007a91660dcf76395d1f4be5ab152f7f41e306e15e46c880f56bb49ca","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"amo.open-system-atoms.dissipative-chiral-state","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Engineered loss can pump atoms into a chosen state, like water settling at the bottom of a bowl. It is unknown whether this works for states with a built-in handedness, such as the quantum Hall states, using only short-range processes.","posed_since":"2015","precise":"Fermions or spins on a 2D lattice evolving under a Lindblad master equation with finite-range jump operators and finite-range Hamiltonian. Determine whether a pure state with nonzero Chern number (or nonzero Hall conductance) can be the unique steady state with a Liouvillian gap that stays finite as $N \\to \\infty$. Known obstructions: quadratic (Gaussian) local Lindbladians cannot do it (Budich, Zoller, Diehl, PRA 2015), and local commuting-projector Hamiltonians have zero Hall conductance (Kapustin, Fidkowski, CMP 2019). Answer: a general no-go proof covering interacting Lindbladians, or an explicit local Lindbladian that works.","problem_ref":null,"references":"","settled_by":"A theorem extending the Gaussian obstruction to interacting finite-range Lindbladians, or a constructed counterexample with a proven size-independent Liouvillian gap.","status_note":"Approximate dissipative schemes for Chern and fractional Chern insulators exist (Liu, Bergholtz, Budich, Phys. Rev. Research 2021), but none gives an exact pure chiral steady state with a finite gap.","title":"Can local dissipation prepare a pure chiral topological state?","topic_ref":"c01d47aa6b153914cd3fb1fd6789e159c512020314bd881d4dec988b5de3df86"},"content_withheld":"false","files":[],"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"3492d9f794a15df3ee2cd6b4bf37368481abd95668552cca82b6cb3117b26e2c","schema":"pubphys.attested/1"},"id_token":null,"id_token_withheld":"false","envelope":{"attested_hash":"f222558bca87ac9fb6666e890badb89a60e1049a1f4dd9c653e69ac9dbf37b0c","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"U03t9bkNJG_TGdJLUXC6K8eKE6bvYn7s9CVPLo-tQjoVzI_mXdyvQkc3ad34iO38Hr8JNcLscjXO2KVMHi4zBA"},"schema":"pubphys.envelope/1"},"ots":{"attested":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEI8iJVi8qHrJ-2Zm6JC624mmDhBJofTdnGU-aaydvzewzwIPJNtI2MBPaLFqo21ZhnE6Ru4oQ-RNWvXaYoMZ0HMmkzCPAgsdfCJGtst8dcvyS2gydfDXsiSvJ9u2LCFkc_qWDzXGAI8SBszkh9r1-eVPhBiWqsL1DUOfBvjTyb-SUlnSl0b3ZUkQjxIKBG0a26oNgpxPGdZUj5dPp3U5eIRu6zxjjuPG1Qz00TCPEgGq_RwHEiOpQh2pT_WRHcCsyInKcc2JIvmb6SzmimiC0I8SBjwX1mn1v0lrKsqzDOtikQv9q6kVbAZnqd0E2evRTK-gjwIAz1dj1zoq3Q3xYVUK230VvgL9_uFVNS120UrX5BlfFcCPEgb1HWQLf7N5Rua2bORFDL2fDBJS7iVOSaHp7adL8jwH8I8SAVG4HLRiZRZ26g7AYBWDSI50GY2TGlNC7pHIYc-vQ3UgjxIOUdEg6sSGuGAwm6byKNwNSH-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_ieLohOiSlAEIqkQqqeoOwFPkmhc5LAqxmFwNJlKolmNI_38B30p5yIDxIKo1Gn-Zyn5b1MLuR7G36SP0g_nU51QaqfUY9lhEGdqyCPEgjtF9fwME1IbtRphT-qLC0hvujIFABwjTZ7w4s-krjuMI8SBrcqVQKzJr3-Or7ocmG4fQ1FKdsx6l806h0C5vxRuRhwjxIMpj0Bimk72oWuaK3-jGhWHCn3MjscgIDx9zWxZQ9ea0CPAgRX5HgEbd2w__6eK6vQEfr_EBG-dGGqCJeb8VvBN_r9II8SDrUQq0P_3RIMF0SxUGjdzmPZB9xUo8Eg_zL63pyUDVOgjxIB00DzZ9Qng0QceJJ_F9izc5bRyu55lPUh3-2VoOpy2ACPEgrA74zq9OS_EO_vifvlqDPPUyYaAxJJae8fQw9_OOt1II8CB0Pk63gwyd_u5K2K1drJW3UxU3mXTBkDKQdutj6_nnEgjxIFf8EhaVa-ubjpYx3wEAcKGxkzfUQq6B-8jimpRd8IqnCPAgy6DmLQtIuWm-zrDRmaSy95vcFWsjvWyppQO7wIWrfC4I8SAQuuTPkAGyvS_wKMy9BtKvnki2puESdY2vXem8hT1uIQjwIBGYo5Vxy-d7U5zKv5vp3Ii7hJPH_BDLCzA13c47p9q7CP_wCHbghVgOFMuNCPAQPZK2lHbTMqcCYUotzOQcmQjwIJ7ruRIs6HnufKxCpmLUgeUl0aUu0ov4_3PqcppS-bddCPEgI530vHzdwz_3o9jYQ3WablSaV64Wf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