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Introduction. The Snirelman theorem. Quantum unique ergodicity ? Pictures. Kolmogorov-Sinai entropy. About the proof. Entropy and the localization of eigenfunctions.
 

Summary: Introduction. The Snirelman theorem. Quantum unique ergodicity ? Pictures. Kolmogorov-Sinai entropy. About the proof.
Entropy and the localization of eigenfunctions.
Nalini Anantharaman
CMLS, ´Ecole Polytechnique
16 octobre 2007
Introduction. The Snirelman theorem. Quantum unique ergodicity ? Pictures. Kolmogorov-Sinai entropy. About the proof.
X a compact riemannian manifold, of dimension d.
k = -kk
k L2(X) = 1
in the limit k - +.
Introduction. The Snirelman theorem. Quantum unique ergodicity ? Pictures. Kolmogorov-Sinai entropy. About the proof.
X a compact riemannian manifold, of dimension d.
k = -kk
k L2(X) = 1
in the limit k - +.
Fig.: A few eigenfunctions of the Bunimovich billiard (Heller, 89).
Introduction. The Snirelman theorem. Quantum unique ergodicity ? Pictures. Kolmogorov-Sinai entropy. About the proof.
We study the weak limits of the probability measures on X,
|k(x)|2
dVol(x)

  

Source: Anantharaman, Nalini - Centre de Mathématiques Laurent Schwartz, École Polytechnique

 

Collections: Mathematics