Upper bounds on the spectral gaps of quasi-periodic Schrödinger operators with Liouville frequencies

DOI10.4171/JST/275zbMath1441.47038arXiv1708.01760MaRDI QIDQ2301858

Wencai Liu, Yunfeng Shi

Publication date: 25 February 2020

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.01760

zbMATH Keywords

upper boundsspectral gapsquasi-periodic Schrödinger operatorsLiouville frequencies

Mathematics Subject Classification ID

Phase transitions (general) in equilibrium statistical mechanics (82B26) Periodic and quasi-periodic flows and diffeomorphisms (37C55) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Related Items (8)

Quantitative reducibility of Gevrey quasi-periodic cocycles and its applications ⋮ Sharp Hölder continuity of the integrated density of states for extended Harper's model with a Liouville frequency ⋮ Homogeneous spectrum of quasi-periodic Gevrey Schrödinger operators with Diophantine frequency ⋮ Exponential upper bounds on the spectral gaps and homogeneous spectrum for the non-critical extended Harper's model ⋮ Almost Mathieu operators with completely resonant phases ⋮ Quantitative inductive estimates for Green's functions of non-self-adjoint matrices ⋮ Polynomial decay of the gap length for \(C^k\) quasi-periodic Schrödinger operators and spectral application ⋮ Exponential decay of the lengths of the spectral gaps for the extended Harper's model with a Liouvillean frequency

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