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Student Analysis Seminar

What is quantum ergodicity?
Monday, October 26, 2020
11:00-11:50 AM
Virtual East Hall Map
Quantum mechanics provides a framework for turning questions about certain dynamics systems into questions about eigenfunctions of certain operators. For example, the Laplacian on a manifold is the operator of interest corresponding to the geodesic flow. A natural question is what the quantum mechanical analogue of ergodicity is. In particular if the geodesic flow on a manifold is ergodic, how does this "show up" in the eigenfunctions of the Laplacian? The answer is that, in a precise sense, "most" eigenfunctions of the Laplacian tend to be "equidistributed" over the entire manifold. In this talk I will motivate, make precise, and sketch a proof of this statement. I hope to keep the talk self-contained; in particular I will not assume that the audience has any background in quantum mechanics or dynamics. Speaker(s): Carsten Peterson (University of Michigan)
Building: East Hall
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics