{"paper":{"title":"Cumulants associated with geometric phases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Bal\\'azs Het\\'enyi, Mohammad Yahyavi","submitted_at":"2013-09-11T20:36:02Z","abstract_excerpt":"The Berry phase can be obtained by taking the continuous limit of a cyclic product $-\\mbox{Im} \\ln \\prod_{I=0}^{M-1} \\langle \\Psi_0({\\boldsymbol\n  \\xi}_I)|\\Psi_0({\\boldsymbol \\xi}_{I+1})\\rangle$, resulting in the circuit integral $i \\oint \\mbox{d}{\\boldsymbol \\xi} \\cdot \\langle \\Psi_0({\\boldsymbol\n  \\xi})|\\nabla_{\\boldsymbol \\xi}|\\Psi_0({\\boldsymbol \\xi}\\rangle$. Considering a parametrized curve ${\\boldsymbol \\xi}(\\chi)$ we show that the product $\\prod_{I=0}^{M-1} \\langle \\Psi_0(\\chi_I)|\\Psi_0( \\chi_{I+1})\\rangle$ can be equated to a cumulant expansion. The first contributing term of this expa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2962","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"}