89 citations · 1.1k across the 43 of their papers we have counts for
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Mathematics of internal waves in a 2D aquarium
Semyon Dyatlov, Jian Wang, Maciej Zworski
Following theoretical and experimental work of Maas et al we consider a linearized model for internal waves in effectively two dimensional aquaria. We provide a precise description…
Macroscopic limits of chaotic eigenfunctions
Semyon Dyatlov
We give an overview of the interplay between the behavior of high energy eigenfunctions of the Laplacian on a compact Riemannian manifold and the dynamical properties of the geodes…
Semiclassical measures for higher dimensional quantum cat maps
Semyon Dyatlov, Malo Jézéquel
Consider a quantum cat map associated to a matrix , which is a common toy model in quantum chaos. We show that the mass of eigenfunction…
Pollicott-Ruelle resolvent and Sobolev regularity
Semyon Dyatlov
In this note we compute the threshold regularity for meromorphic continuation of the Pollicott--Ruelle resolvent of an Anosov flow as an operator on anisotropic Sobolev spaces, in…
Around quantum ergodicity
Semyon Dyatlov
We discuss Shnirelman's Quantum Ergodicity Theorem, giving an outline of a proof and an overview of some of the recent developments in mathematical Quantum Chaos.