{"paper":{"title":"Waves in Honeycomb Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","math-ph","math.AP","math.MP","quant-ph"],"primary_cat":"nlin.PS","authors_text":"Charles L. Fefferman, Michael I. Weinstein","submitted_at":"2012-12-30T03:32:30Z","abstract_excerpt":"We review recent work of the authors on the non-relativistic Schr\\\"odinger equation with a honeycomb lattice potential, $V$. In particular, we summarize results on (i) the existence of Dirac points, conical singularities in dispersion surfaces of $H_V=-\\Delta+V$ and (ii) the two-dimensional Dirac equations, as a large, but finite time, effective description of $e^{-iH_Vt}\\psi_0$, for data $\\psi_0$, which is spectrally localized at a Dirac point. We conclude with a formal derivation and discussion of the effective large time evolution for the nonlinear Schr\\\"odinger - Gross Pitaevskii equation "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6684","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"}