{"paper":{"title":"Statistics of resonances and of delay times in quasiperiodic Schr\"odinger equations","license":"","headline":"","cross_cats":["cond-mat.dis-nn","nlin.CD"],"primary_cat":"cond-mat.mes-hall","authors_text":"A. Ossipov, F. Steinbach, T. Geisel, Tsampikos Kottos","submitted_at":"2000-07-06T15:28:37Z","abstract_excerpt":"We study the statistical distributions of the resonance widths ${\\cal P} (\\Gamma)$, and of delay times ${\\cal P} (\\tau)$ in one dimensional quasi-periodic tight-binding systems with one open channel. Both quantities are found to decay algebraically as $\\Gamma^{-\\alpha}$, and $\\tau^{-\\gamma}$ on small and large scales respectively. The exponents $\\alpha$, and $\\gamma$ are related to the fractal dimension $D_0^E$ of the spectrum of the closed system as $\\alpha=1+D_0^E$ and $\\gamma=2-D_0^E$. Our results are verified for the Harper model at the metal-insulator transition and for Fibonacci lattices"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0007105","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"}