{"paper":{"title":"Semiclassics for matrix Hamiltonians: The Gutzwiller trace formula and applications to the graphene-type systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mes-hall","authors_text":"M. Vogl, O. Pankratov, S. Shallcross","submitted_at":"2016-11-27T17:41:48Z","abstract_excerpt":"We have extended the semi-classical theory to include a general account of matrix valued Hamiltonians, i.e. those that describe quantum systems with internal degrees of freedoms, based on a generalization of the Gutzwiller trace formula for a $n\\times n$ dimensional Hamiltonian $H(\\hat{\\boldsymbol p},\\hat{\\boldsymbol q})$. The classical dynamics is governed by $n$ Hamilton-Jacobi (HJ) equations, that act in a phase space endowed with a classical Berry curvature encoding anholonomy in the parallel transport of the eigenvectors of $H(\\hat{\\boldsymbol p}\\to\\boldsymbol p,\\hat{\\boldsymbol q}\\to\\bol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08879","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"}