{"paper":{"title":"Analyzing the Positivity Preservation of Numerical Methods for the Liouville-von Neumann Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"quant-ph","authors_text":"Christian Jirauschek, Michael Riesch","submitted_at":"2018-08-01T16:58:16Z","abstract_excerpt":"The density matrix is a widely used tool in quantum mechanics. In order to determine its evolution with respect to time, the Liouville-von Neumann equation must be solved. However, analytic solutions of this differential equation exist only for simple cases. Additionally, if the equation is coupled to Maxwell's equations to model light-matter interaction, the resulting equation set -- the Maxwell-Bloch or Maxwell-Liouville-von Neumann (MLN) equations -- becomes nonlinear. In these advanced cases, numerical methods are required. Since the density matrix has certain mathematical properties, the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00416","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"}