{"paper":{"title":"Oscillating potential well in complex plane and the adiabatic theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Stefano Longhi","submitted_at":"2017-10-12T09:54:56Z","abstract_excerpt":"A quantum particle in a slowly-changing potential well $V(x,t)=V(x-x_0(\\epsilon t))$, periodically shaken in time at a slow frequency $\\epsilon$, provides an important quantum mechanical system where the adiabatic theorem fails to predict the asymptotic dynamics over time scales longer than $ \\sim 1 / \\epsilon$. Specifically, we consider a double-well potential $V(x)$ sustaining two bound states spaced in frequency by $\\omega_0$ and periodically-shaken in complex plane. Two different spatial displacements $x_0(t)$ are assumed: the real spatial displacement $x_0(\\epsilon t)=A \\sin (\\epsilon t)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04429","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"}