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4:00 pm Wednesday, October 23, 2013 Geometry-Analysis Seminar: Dynamics of Unitary Operatorsby
Jake Fillman (Rice University) in HB 227- I will discuss dynamical systems defined by the iteration of a unitary operator on a Hilbert space. The discussion will center around the interplay between spectral characteristics of the unitary operator in question and the dynamical properties of the iteration thereof. The primary result is a natural extension of the Guarneri-Combes-Last bound: uniform H\"older continuity of a spectral measure implies quantitative lower bounds on the spreading of the corresponding wave packet. Together with results of Damanik, Munger, Ong, and Yessen, this allows us to prove explicit quantitative lower bounds for the spreading of the quantum walk corresponding to a two-sided CMV matrix which has Fibonacci Verblunsky coefficients.
Submitted by damanik@rice.edu |