Arithmetic Phase Transitions For Mosaic Maryland Model

TL;DR

This paper precisely characterizes the spectral types of the Mosaic Maryland model across all irrational frequencies, revealing an arithmetic phase transition in a quasi-periodic unbounded model with a non-monotone potential.

Contribution

It provides a detailed description of spectral types for the Mosaic Maryland model, demonstrating an arithmetic phase transition in a complex quasi-periodic setting.

Findings

Spectral types are fully characterized for all irrational frequencies.

Identifies an arithmetic phase transition in the model.

Advances understanding of spectral behavior in non-monotone quasi-periodic systems.

Abstract

We give a precise description of spectral types of the Mosaic Maryland model with any irrational frequency, which provides a quasi-periodic unbounded model with non-monotone potential has arithmetic phase transition.