{"paper":{"title":"Derivation of the Biot-Savart equation from the Nonlinear Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.PS"],"primary_cat":"physics.flu-dyn","authors_text":"Miguel D. Bustamante, Sergey V. Nazarenko","submitted_at":"2015-07-28T15:19:17Z","abstract_excerpt":"We present a systematic derivation of the Biot-Savart equation from the Nonlinear Schr\\\"odinger equation, in the limit when the curvature radius of vortex lines and the inter-vortex distance are much greater than the vortex healing length, or core radius. We derive the Biot-Savart equations in Hamiltonian form with Hamiltonian expressed in terms of vortex lines, $$ H= \\frac{\\kappa^2}{8 \\pi}\\int_{|{\\bf s}-{\\bf s}'|>\\xi_*} \\frac{d{\\bf s} \\cdot d {\\bf s}'}{|{\\bf s}-{\\bf s}'|} \\,,$$ with cut-off length $\\xi_* \\approx 0.3416293 /\\sqrt{\\rho_0},$ where $\\rho_0$ is the background condensate density fa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07806","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"}