{"paper":{"title":"Unusual eigenvalue spectrum and relaxation in the L\\'{e}vy Ornstein-Uhlenbeck process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Deepika Janakiraman, K. L. Sebastian","submitted_at":"2014-06-02T19:07:36Z","abstract_excerpt":"We consider the rates of relaxation of a particle in a harmonic well, subject to L\\'evy noise characterized by its L\\'evy index $\\mu$. Using the propagator for this L\\'evy Ornstein-Uhlenbeck process (LOUP), we show that the eigenvalue spectrum of the associated Fokker-Planck operator has the form $(n+m\\mu)\\nu$ where $\\nu$ is the force constant characterizing the well, and $n,m\\in\\mathbb{N}$. If $\\mu$ is irrational, the eigenvalues are all non-degenerate, but rational $\\mu$ can lead to degeneracy. The maximum degeneracy is shown to be two. The left eigenfunctions of the fractional Fokker-Planck"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0478","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"}