{"paper":{"title":"Kibble-Zurek mechanism with a single particle: dynamics of the localization-delocalization transition in the Aubry-Andr\\'e model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Aritra Sinha, Jacek Dziarmaga, Marek M. Rams","submitted_at":"2018-11-13T19:04:42Z","abstract_excerpt":"The Aubry-Andr\\'e 1D lattice model describes a particle hopping in a pseudo-random potential. Depending on its strength $\\lambda$, all eigenstates are either localized ($\\lambda>1$) or delocalized ($\\lambda<1$). Near the transition, the localization length diverges like $\\xi\\sim(\\lambda-1)^{-\\nu}$ with $\\nu=1$. We show that when the particle is initially prepared in a localized ground state and the potential strength is slowly ramped down across the transition, then -- in analogy with the Kibble-Zurek mechanism -- it enters the delocalized phase having finite localization length $\\hat\\xi\\sim\\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05496","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"}