{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"e7d589d63e01c19367d392a3c99e4a39a29c387ef468545153a90c2b6324cfcf","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["abb802fc838fd0d5472c1408bc48ac2e5a2dfcc00a133f080d5994c8a42d9e7a","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"aa8b6171c5b4853d33b22c664caafa9e6a941c564df763140bafd4696e50d89a","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":["ai:gpt-5.5"],"external_id":"stat.fput-thermalization.dnls-negative-temperature","kind":"well-posed","literature_status":"partially-resolved","n":"2","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 $h_{\\mathrm{inf}} = g a^2$, 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 $h - h_{\\mathrm{inf}}$. An answer is the asymptotic law, or a proof that the relaxation time diverges with $N$.","problem_ref":"abb802fc838fd0d5472c1408bc48ac2e5a2dfcc00a133f080d5994c8a42d9e7a","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 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