{"paper":{"title":"Divergence of the logarithm of a unimodular monodromy matrix near the edges of the Brillouin zone","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.mtrl-sci","authors_text":"A. A. Kutsenko, A. L. Shuvalov, Andrew N. Norris","submitted_at":"2009-11-10T23:44:24Z","abstract_excerpt":"A first-order differential system with matrix of periodic coefficients $Q(y)=Q(y+T) $ is studied for time-harmonic elastic waves in a unidirectionally periodic medium, for which the monodromy matrix $M(\\omega) $ implies a propagator of the wave field over a period. The main interest in the matrix logarithm $\\ln M(\\omega) $ is due to the fact that it yields the 'effective' matrix $Q_{eff}(\\omega) $ of the dynamic-homogenization method. For the typical case of a unimodular matrix $M(\\omega)$ ($\\det M=1$), it is established that the components of $\\ln M(\\omega) $ diverge as $(\\omega -\\omega_0)^{-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2029","kind":"arxiv","version":1},"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"}