{"paper":{"title":"Propagation of Wigner functions for the Schroedinger equation with a perturbed periodic potential","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Gianluca Panati, Stefan Teufel","submitted_at":"2004-03-19T13:50:19Z","abstract_excerpt":"Let $V_\\Gamma$ be a lattice periodic potential and $A$ and $\\phi$ external electromagnetic potentials which vary slowly on the scale set by the lattice spacing. It is shown that the Wigner function of a solution of the Schroedinger equation with Hamiltonian operator $H = {1/2} (-\\I\\nabla_x - A(\\epsilon x))^2 + V_\\Gamma (x) + \\phi(\\epsilon x)$ propagates along the flow of the semiclassical model of solid states physics up an error of order $\\epsilon$. If $\\epsilon$-dependent corrections to the flow are taken into account, the error is improved to order $\\epsilon^2$. We also discuss the propagat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0403037","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"}