{"paper":{"title":"Three-dimensional stability of leapfrogging quantum vortex rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.PS"],"primary_cat":"cond-mat.other","authors_text":"Victor P. Ruban","submitted_at":"2018-06-21T11:25:02Z","abstract_excerpt":"It is shown by numerical simulations within a regularized Biot-Savart law that dynamical systems of two or three leapfrogging coaxial quantum vortex rings having a core width $\\xi$ and initially placed near a torus of radii $R_0$ and $r_0$, can be three-dimensionally (quasi-)stable in some regions of parameters $\\Lambda=\\ln(R_0/\\xi)$ and $W=r_0/R_0$. At fixed $\\Lambda$, stable bands on $W$ are intervals between non-overlapping main parametric resonances for different (integer) azimuthal wave numbers $m$. The stable intervals are most wide ($\\Delta W\\sim$ 0.01--0.05) between $m$-pairs $(1,2)$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.08173","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"}