Entropy of semiclassical measures in dimension 2

TL;DR

This paper investigates the entropy characteristics of eigenfunctions of the Laplacian on compact Anosov surfaces, establishing a lower bound for the Kolmogorov-Sinai entropy of associated semiclassical measures.

Contribution

It provides a novel lower bound for the entropy of semiclassical measures in the context of Anosov surfaces, linking quantum eigenfunctions to classical dynamical properties.

Findings

Kolmogorov-Sinai entropy of semiclassical measures is at least half of the Ruelle upper bound.

Establishes a quantitative connection between quantum eigenfunctions and classical chaotic dynamics.

Advances understanding of quantum chaos in negatively curved surfaces.

Abstract

We study the asymptotic properties of eigenfunctions of the Laplacian in the case of a compact Riemannian surface of Anosov type. We show that the Kolmogorov-Sinai entropy of a semiclassical measure for the geodesic flow is bounded from below by half of the Ruelle upper bound