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The Robust Ten Martini Problem

Year: 2026

Type: preprint

Abstract: We solve the robust ten martini problem: Cantor spectrum with no arithmetic restriction on the irrational frequency for Type I analytic one-frequency quasiperiodic Schrodinger operators. We introduce Type I through a new acceleration-type quantity with stability under analytic perturbations. This yields a global open class of analytic potentials whose associated operators have Cantor spectrum for every irrational frequency.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.15812

Authors: Ge, Lingrui, Jitomirskaya, Svetlana, You, Jiangong

Institution: Peking University

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Georgia Institute of Technology, National Natural Science Foundation of China, Peking University, Nankai Zhide Foundation, Fundamental Research Funds for the Central Universities

Awards: Spectral Transitions and Critical Phenomena, G1916587917, G5457419779, G6609366462, FRG: Collaborative Research: Non-Perturbative Analysis for Multi-Dimensional Quasiperiodic Systems, G7462286394

OpenAlex ID: W7213343279

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