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Measure of the spectrum of the extended Harper's model

Date: 
Tuesday 7th April 2015 - 16:00 to 16:25
Venue: 
INI Seminar Room 1
Abstract: 
Co-author: Svetlana Jitomirskaya (University of California, Irvine)

In this talk, we will discuss the measure of the spectrum of the extended Harper's model(EHM). The measure of the spectrum of the Harper's model, which in mathematics is better known as the almost Mathieu operator(AMO), is know to be |4-2a| where a is the coupling constant. The way of calculating the measure mainly relies on the analysis of the AMO with rational frequency and the continuity argument. Here we focus on how to calculate the measure of the spectrum of the EHM with rational frequency, therefore implying the result of irrtional frequency.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons