{"paper":{"title":"First passage time distribution in underdamped harmonic oscillators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Alberto Imparato, Aubin Archambault, Caroline Crauste-Thibierge, Ludovic Bellon, Sergio Ciliberto","submitted_at":"2026-07-01T19:11:09Z","abstract_excerpt":"We derive the distribution of the first passage time $t_{fp}$ for the position $x$ of an underdamped harmonic oscillator to overcome a threshold $x_B$. As the $t_{fp}$ distribution depends on the oscillator quality factor $Q$ different approaches are used. At very large quality factor ($Q\\gg 100$) and intermediate and long $t_{fp}$ the proof is based on an energy diffusion model, whereas at medium quality factor ($Q\\sim 10$) the proof is based on the study of the eigenvalues of the Kramers linear differential operator with absorbing boundary conditions. For all $Q$ and short $t_{fp}$ we use a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01405","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/2607.01405/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"}