{"paper":{"title":"Stable and unstable vortex knots in a trapped Bose-Einstein condensate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.PS"],"primary_cat":"cond-mat.quant-gas","authors_text":"Victor P. Ruban","submitted_at":"2017-11-01T10:42:46Z","abstract_excerpt":"The dynamics of a quantum vortex torus knot ${\\cal T}_{P,Q}$ and similar knots in an atomic Bose-Einstein condensate at zero temperature in the Thomas-Fermi regime has been considered in the hydrodynamic approximation. The condensate has a spatially nonuniform equilibrium density profile $\\rho(z,r)$ due to an external axisymmetric potential. It is assumed that $z_*=0$, $r_*=1$ is a maximum point for function $r\\rho(z,r)$, with $\\delta (r\\rho)\\approx-(\\alpha-\\epsilon) z^2/2 -(\\alpha+\\epsilon) (\\delta r)^2/2$ at small $z$ and $\\delta r$. Configuration of knot in the cylindrical coordinates is sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00280","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"}