{"paper":{"title":"A Sampling-Based Adaptive Rank Approach to the Wigner-Poisson System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Andrew Christlieb, Jing-Mei Qiu, Nanyi Zheng, Sining Gong","submitted_at":"2025-06-26T14:29:12Z","abstract_excerpt":"We develop a mass-conserving, adaptive-rank solver for the 1D1V Wigner-Poisson system. Our work is motivated by applications to the study of the stopping power of $\\alpha$ particles at the National Ignition Facility (NIF). In this regime, electrons are in a warm dense state, requiring more than a standard kinetic model. They are hot enough to neglect Pauli exclusion, yet quantum enough to require accounting for uncertainty. The Wigner-Poisson system captures these effects but presents challenges due to its nonlocal nature. Based on a second-order Strang splitting method, we first design a full"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.21314","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.21314/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}