Entropy of eigenfunctions

Nalini Anantharaman (1) , Herbert Koch (2) , Stéphane Nonnenmacher (3)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 Rheinische Friedrich-Wilhelms-Universität Bonn
3 IPHT - Institut de Physique Théorique - UMR CNRS 3681

We study the high--energy limit for eigenfunctions of the laplacian, on a compact negatively curved manifold. We review the recent result of Anantharaman-Nonnenmacher giving a lower bound on the Kolmogorov-Sinai entropy of semiclassical measures, and improve this lower bound in the case of variable negative curvature.

Keywords: semiclassical measure; KS entropy; Anosov geodesic flow; quantum chaos

Domains: Mathematical Physics [math-ph]; Dynamical Systems [math.DS]; Chaotic Dynamics [nlin.CD]; Mathematical Physics [math-ph]

Nalini Anantharaman, Herbert Koch, Stéphane Nonnenmacher. Entropy of eigenfunctions. New Trends in Mathematical Physics; Sidoravičius, V. (eds), Springer, pp.1-22, 2009, Print ISBN 978-90-481-2809-9; Online ISBN 978-90-481-2810-5. ⟨10.1007/978-90-481-2810-5_1⟩. ⟨hal-00141310⟩