{"paper":{"title":"Hofstadter quasicrystals, hidden symmetries and irrational quantum oscillations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mes-hall","authors_text":"Grigor Adamyan, Kirill Kozlov, Leonid Levitov, Mariia Kryvoruchko, Yelizaveta Kulynych","submitted_at":"2023-11-28T17:12:41Z","abstract_excerpt":"Landau levels perturbed by a periodic potential is a prime setting to design quantum systems with exotic fractal spectra. Motivated by recent advances in twistronics, we introduce `Hofstadter quasicrystal' problem describing Landau levels perturbed by a set of incommensurate cosine waves. We illustrate the underlying physics for moir\\'{e} quasicrystals with octagonal and dodecagonal symmetries, finding spectra that are vastly more complex than the Hofstadter spectrum. Surprisingly, due to the high spatial symmetry, the quasicrystal problem exhibits hidden `inner' symmetry arising at special `m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.16967","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/2311.16967/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"}