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Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)$
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Christopher D. Sogge

Print publication date: 2014

Print ISBN-13: 9780691160757

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691160757.001.0001

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Classical and quantum ergodicity

Classical and quantum ergodicity

(p.141) Chapter Six Classical and quantum ergodicity
Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)

Christopher D. Sogge

Princeton University Press

This chapter proves results involving the quantum ergodicity of certain high-frequency eigenfunctions. Ergodic theory originally arose in the work of physicists studying statistical mechanics at the end of the nineteenth century. The word ergodic has as its roots two Greek words: ergon, meaning work or energy, and hodos, meaning path or way. Even though ergodic theory's initial development was motivated by physical problems, it has become an important branch of pure mathematics that studies dynamical systems possessing an invariant measure. Thus, this chapter first presents some of the basic limit theorems that are key to the classical theory. It then turns to quantum ergodicity.

Keywords:   quantum ergodicity, high frequency eigenfunctions, ergodic theory, classical ergodicity, invariant measure, limit theorems, quantum chaos

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