Entropy of chaotic eigenstates

Stéphane Nonnenmacher (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

These notes present a recent approach to study the high-frequency eigenstates of the Laplacian on compact Riemannian manifolds of negative sectional curvature. The main result is a lower bound on the Kolmogorov-Sinai entropy of the semiclassical measures associated with sequences of eigenstates, showing that high-frequency eigenstates cannot be too localized. The method is extended to the case of semiclassical Hamiltonian operators for which the classical flow in some energy range is of Anosov type, and to the case of quantized Anosov diffeomorphisms on the torus.

Mots clés: quantum chaos; quantum unique ergodicity; entropic uncertainty principle

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]; Dynamique Chaotique [nlin.CD]; Systèmes dynamiques [math.DS]

Stéphane Nonnenmacher. Entropy of chaotic eigenstates. D.Jakobson, S.Nonnenmacher, I.Polterovich. Actes de colloque, CRM - AMS, pp.1-42, 2010, CMR Proceedings and Lecture Notes 52, 978-0-8218-4778-7. ⟨hal-00476985⟩