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Session S30 - Mathematical Methods in Quantum Mechanics

Thursday, July 15, 16:30 ~ 16:55 UTC-3

Zero measure spectrum for multi-frequency Schrödinger operators

Jake Fillman

Texas State University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Building on works of Berthé--Steiner--Thuswaldner and Fogg--Nous we show that on the two-dimensional torus, Lebesgue almost every translation admits a natural coding such that the associated subshift satisfies the Boshernitzan criterion. As a consequence we show that for these torus translations, every quasi-periodic potential can be approximated uniformly by one for which the associated Schrödinger operator has Cantor spectrum of zero Lebesgue measure.

Joint work with Jon Chaika (University of Utah), David Damanik (Rice University) and Philipp Gohlke (Universität Bielefeld).

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