{"paper":{"title":"The non-equilibrium distribution function of particles and anti-particles created in strong fields","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"A. V. Prozorkevich, Dubna, D. V. Vinnik (Saratov State University, Russia), S. A. Smolyansky, V. A. Mizerny, V.D. Toneev (Joint Institute for Nuclear Research","submitted_at":"1999-11-10T17:19:44Z","abstract_excerpt":"We investigate the quantum Vlasov equation with a source term describing the spontaneous particle creation in strong fields. The back-reaction problem is treated by solving this kinetic equation together with the Maxwell equation which determines the induced time-dependent electric field in the system. The evolution of distribution functions for bosons and fermions is studied numerically. We found that the system shows a regular dynamic behavior if the back-reaction is neglected. But if the back-reaction is included, it is not the case and some stochastic features are clearly revealed in the n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/9911303","kind":"arxiv","version":3},"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"}