Séminaire Analyse Numérique et EDP
Ruling out periodicity in quantum chaos
19
June 2025
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Intervenant : Alex Cohen
Institution : Massachusetts Institute of Technology
Heure : 14h00 - 15h00
Lieu : 3L8

A central question in quantum chaos is to understand the behavior of high-frequency Laplace eigenfunctions on hyperbolic manifolds. Quantum cat maps are a model system that behave like hyperbolic manifolds: the known tools apply equally well to both systems. However, some quantum cat maps exhibit a strange periodicity, resulting in concentration of eigenfunctions—behavior not expected for eigenfunctions on hyperbolic manifolds. We discuss new work distinguishing these two systems. The key ingredient is an uncertainty principle that distinguishes the Fourier transform from a modified Fourier transform with nonlinear phase function. 

Joint with Semyon Dyatlov. 

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