The Spectrum of the Almost Mathieu Operator

2009/08/07 by David Damanik, Damanik, David
Mathematics · #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical functions and polynomials #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.0908.1093

openalex publication_date 2009/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

These notes are based on a series of six lectures, given during my stay at the CRC 701 in June/July 2008. The lecture series intended to give a survey of some of the results for the almost Mathieu operator that have been obtained since the early 1980's. Specifically, the metal-insulator transition is discussed in detail, along with its relation to the ten Martini problem via duality and reducibility.

Related

• The absolutely continuous spectrum of the almost Mathieu operator
• On the spectrum of critical almost Mathieu operators in the rational case
• Persistence of gaps in the spectrum of certain almost periodic operators
• Dry Ten Martini Problem in the non-critical case
• Second Phase transition line