Distributions of Resonances of Supercritical Quasi-Periodic Operators

DOI10.1093/IMRN/RNAD006arXiv2208.06944MaRDI QIDQ6142525

Wencai Liu

Publication date: 26 January 2024

Published in: IMRN. International Mathematics Research Notices (Search for Journal in Brave)

Abstract: We discover that the distribution of (frequency and phase) resonances plays a role in determining the spectral type of supercritical quasi-periodic Schr"odinger operators. In particular, we disprove the second spectral transition line conjecture of Jitomirskaya in the early 1990s.

Full work available at URL: https://arxiv.org/abs/2208.06944

Mathematics Subject Classification ID

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