{"paper":{"title":"Exact Analysis of the Adiabatic Invariants in Time-Dependent Harmonic Oscillator","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Marko Robnik, Valery G. Romanovski","submitted_at":"2005-06-16T14:57:32Z","abstract_excerpt":"The theory of adiabatic invariants has a long history and important applications in physics but is rarely rigorous. Here we treat exactly the general time-dependent 1-D harmonic oscillator, $\\ddot{q} + \\omega^2(t) q=0$ which cannot be solved in general. We follow the time-evolution of an initial ensemble of phase points with sharply defined energy $E_0$ and calculate rigorously the distribution of energy $E_1$ after time $T$, and all its moments, especially its average value $\\bar{E_1}$ and variance $\\mu^2$. Using our exact WKB-theory to all orders we get the exact result for the leading asymp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0506033","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":""},"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"}