{"paper":{"title":"Number-theoretic aspects of 1D localization: \"popcorn function\" with Lifshitz tails and its continuous approximation by the Dedekind $\\eta$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn"],"primary_cat":"math.NT","authors_text":"K. Polovnikov, S. Nechaev","submitted_at":"2017-02-22T11:29:20Z","abstract_excerpt":"We discuss the number-theoretic properties of distributions appearing in physical systems when an observable is a quotient of two independent exponentially weighted integers. The spectral density of ensemble of linear polymer chains distributed with the law $\\sim f^L$ ($0<f<1$), where $L$ is the chain length, serves as a particular example. At $f\\to 1$, the spectral density can be expressed through the discontinuous at all rational points, Thomae (\"popcorn\") function. We suggest a continuous approximation of the popcorn function, based on the Dedekind $\\eta$-function near the real axis. Moreov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06757","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"}