Distributions of resonances of supercritical quasi-periodic operators

2022/08/14 by Liu, Wencai
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2208.06944

Abstract

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

Related

• Sharp Spectral Gaps, Arithmetic Localization, and Reducibility via Resonance Analys
• Subcritical behavior for quasi-periodic Schrödinger cocycles with trigonometric potentials
• Asymptotics of spectral gaps of quasi-periodic Schrödinger operators
• On localization and the spectrum of multi-frequency quasi-periodic operators
• Coexistence of ac and pp spectrum for kicked quasi-periodic potentials