{"paper":{"title":"Bound on the exponential growth rate of out-of-time-ordered correlators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Masahito Ueda, Naoto Tsuji, Tomohiro Shitara","submitted_at":"2017-06-28T08:05:27Z","abstract_excerpt":"It has been conjectured by Maldacena, Shenker, and Stanford [J. High Energy Phys.~08 (2016) 106] that the exponential growth rate of the out-of-time-ordered correlator (OTOC) $F(t)$ has a universal upper bound $2\\pi k_B T/\\hbar$. Here we introduce a one-parameter family of out-of-time-ordered correlators $F_\\gamma(t)$ ($0\\leq\\gamma\\leq 1$), which has as good properties as $F(t)$ as a regularization of the out-of-time-ordered part of the squared commutator $\\langle [A(t), B(0)]^2\\rangle$ that diagnoses quantum many-body chaos, and coincides with $F(t)$ at $\\gamma=1/2$. We rigorously prove that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09160","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"}