{"paper":{"title":"Generators of Detailed Balance Quantum Markov Semigroups","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Franco Fagnola, Veronica Umanita","submitted_at":"2007-07-14T11:02:27Z","abstract_excerpt":"For a quantum Markov semigroup $\\T$ on the algebra $\\B$ with a faithful invariant state $\\rho$, we can define an adjoint $\\widetilde{\\T}$ with respect to the scalar product determined by $\\rho$. In this paper, we solve the open problems of characterising adjoints $\\widetilde{\\T}$ that are also a quantum Markov semigroup and satisfy the detailed balance condition in terms of the operators $H,L_k$ in the Gorini Kossakowski Sudarshan Lindblad representation $\\Ll(x)=i[H,x] - {1/2}\\sum_k(L^*_kL_k x-2L^*_kxL_k + xL^*_kL_k)$ of the generator of $\\T$. We study the adjoint semigroup with respect to bot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.2147","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"}