{"paper":{"title":"Nonlinear von Neumann-type equations: Darboux invariance and spectra","license":"","headline":"","cross_cats":["nlin.SI","solv-int"],"primary_cat":"quant-ph","authors_text":"Maciej Kuna, Marek Czachor, Sergiej B. Leble (Politechnika Gdanska)","submitted_at":"1998-10-07T17:06:03Z","abstract_excerpt":"Generalized Euler-Arnold-von Neumann density matrix equations can be solved by a binary Darboux transformation given here in a new form: $\\rho[1]=e^{P\\ln(\\mu/\\nu)}\\rho e^{-P\\ln(\\mu/\\nu)}$ where $P=P^2$ is explicitly constructed in terms of conjugated Lax pairs, and $\\mu$, $\\nu$ are complex. As a result spectra of $\\rho$ and $\\rho[1]$ are identical. Transformations allowing to shift and rescale spectrum of a solution are introduced, and a class of stationary seed solutions is discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9810023","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}