{"paper":{"title":"Quantum Boltzmann equation for spin-dependent reactions in the kinetic regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Christian B. Mendl, Herbert Spohn, Markus Kotulla, Martin L.R. F\\\"urst","submitted_at":"2014-11-10T20:42:14Z","abstract_excerpt":"We derive and analyze an effective quantum Boltzmann equation in the kinetic regime for the interactions of four distinguishable types of fermionic spin-$\\frac{1}{2}$ particles, starting from a general quantum field Hamiltonian. Each particle type is described by a time-dependent, $2 \\times 2$ spin-density (\"Wigner\") matrix. We show that density and energy conservation laws as well as the H-theorem hold, and enumerate additional conservation laws depending on the interaction. The conserved quantities characterize the $t \\to \\infty$ thermal (Fermi-Dirac) equilibrium state. We illustrate the app"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2576","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"}