{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"7b2709765e1671862ef4a34c669c2af62db05bc833a5fec007af4aa8e5c6739d","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"9c082977d830d0311478f4785946fcfe24aca518a537df41e7b2348c0e5e15a9","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"stat.fput-thermalization.dnls-negative-temperature","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"A chain of coupled nonlinear wave sites can be given so much energy per particle that its temperature formally becomes negative, and energy then gathers into a few tall localized peaks called breathers. Whether the chain ever settles into equilibrium from there, and how long it takes, is not known.","posed_since":"2000","precise":"For the DNLS chain $H = \\sum_n [ (\\psi_n* \\psi_{(n+1)} + \\mathrm{c.c.}) + (g/2)\\left|\\psi_n\\right|^4 ]$ with conserved norm density $a$ and energy density $h$ above the infinite-temperature line h_inf = g a^2, determine whether isolated dynamics from generic initial data relaxes to the microcanonical equilibrium (one breather holding a macroscopic fraction of the norm on an infinite-temperature background), and give the scaling of the relaxation time with chain length $N$ and with h - h_inf. An answer is the asymptotic law, or a proof that the relaxation time diverges with $N$.","problem_ref":null,"references":"","settled_by":"Simulations at increasing N that follow breather and background statistics to the predicted microcanonical state, with a theory of breather growth rates that reproduces the measured times.","status_note":"The microcanonical equilibrium above the line was derived in 2021 (Gradenigo, Iubini, Livi, Majumdar, J. Stat. Mech. 023201, arXiv:1910.07461), and an adiabatic invariant of tall breathers was shown to make relaxation extremely slow (Iubini et al., Phys. Rev. Lett. 122, 084102, 2019); the large-N law is not established.","title":"Relaxation of negative-temperature states in the discrete nonlinear Schrodinger chain","topic_ref":"b026e7f128afdc43ebc73cc909210ea680a0ba040cd45dc5b34d5a420020f836"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"abb802fc838fd0d5472c1408bc48ac2e5a2dfcc00a133f080d5994c8a42d9e7a","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"8baaa382e4b14be53959d6a5fb6ba4412bd63684ee5cdf4ae38361324beb7a63","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"spNyhTHNrhm3TCODFY_9_FfgIr89Q1P3h6rAWGPMXb_fCTMmIGDJeO645saHYn8ZZj7NHZ4W7wRFJEEneIPwBw"},"schema":"pubphys.envelope/1"},"record_hash":"abb802fc838fd0d5472c1408bc48ac2e5a2dfcc00a133f080d5994c8a42d9e7a","leaf_index":2079}