{"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"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"3492d9f794a15df3ee2cd6b4bf37368481abd95668552cca82b6cb3117b26e2c","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"f222558bca87ac9fb6666e890badb89a60e1049a1f4dd9c653e69ac9dbf37b0c","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"U03t9bkNJG_TGdJLUXC6K8eKE6bvYn7s9CVPLo-tQjoVzI_mXdyvQkc3ad34iO38Hr8JNcLscjXO2KVMHi4zBA"},"schema":"pubphys.envelope/1"},"record_hash":"3492d9f794a15df3ee2cd6b4bf37368481abd95668552cca82b6cb3117b26e2c","leaf_index":437}