{"paper":{"title":"Growth of Sobolev norms in quasi integrable quantum systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Beatrice Langella, Dario Bambusi","submitted_at":"2022-02-09T15:07:45Z","abstract_excerpt":"We prove an abstract result giving a $\\langle t \\rangle^\\varepsilon$ upper bound on the growth of the Sobolev norms of a time-dependent Schr\\\"odinger equation of the form ${i} \\dot \\psi = H_0 \\psi + V (t)\\psi$. Here $H_0$ is assumed to be the Hamiltonian of a steep quantum integrable system and to be a pseudodifferential operator of order ${\\tt d} > 1$; $V (t)$ is a time-dependent family of pseudodifferential operators, unbounded, but of order ${\\tt b} < {\\tt d}$. The abstract theorem is then applied to perturbations of the quantum anharmonic oscillators in dimension 2 and to perturbations of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.04505","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2202.04505/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"}