Quantum Flux and Quantum Ergodicity for Cross Sections

Hans Christianson; John Toth

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arXiv · 2404.02296

Quantum Flux and Quantum Ergodicity for Cross Sections

Hans Christianson·John Toth

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Abstract

For sequences of quantum ergodic eigenfunctions, we define the quantum flux norm associated to a codimension $1$ submanifold $\Sigma$ of a non-degenerate energy surface. We prove restrictions of eigenfunctions to $\Sigma$, realized using the quantum flux norm, are quantum ergodic. We compare this result to known results from \cite{CTZ} in the case of Euclidean domains and hyperfurfaces. As a further application, we consider complexified analytic eigenfunctions and prove a second microlocal analogue of \cite{CTZ} in that context.

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Hans Christianson, John Toth. 2024-04-02. Quantum Flux and Quantum Ergodicity for Cross Sections. https://arxiv.org/abs/2404.02296

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