Entropy and localization of eigenfunctions
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2006-2007), Talk no. 4, 17 p.
Anantharaman, Nalini 1

1 CMLS, École Polytechnique, 91128 Palaiseau Cedex
@article{SEDP_2006-2007____A4_0,
     author = {Anantharaman, Nalini},
     title = {Entropy and localization of eigenfunctions},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
     note = {talk:4},
     pages = {1--17},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2006-2007},
     mrnumber = {2385191},
     language = {en},
     url = {http://www.numdam.org/item/SEDP_2006-2007____A4_0/}
}
TY  - JOUR
AU  - Anantharaman, Nalini
TI  - Entropy and localization of eigenfunctions
JO  - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
N1  - talk:4
PY  - 2006-2007
SP  - 1
EP  - 17
PB  - Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - http://www.numdam.org/item/SEDP_2006-2007____A4_0/
LA  - en
ID  - SEDP_2006-2007____A4_0
ER  - 
%0 Journal Article
%A Anantharaman, Nalini
%T Entropy and localization of eigenfunctions
%J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
%Z talk:4
%D 2006-2007
%P 1-17
%I Centre de mathématiques Laurent Schwartz, École polytechnique
%U http://www.numdam.org/item/SEDP_2006-2007____A4_0/
%G en
%F SEDP_2006-2007____A4_0
Anantharaman, Nalini. Entropy and localization of eigenfunctions. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2006-2007), Talk no. 4, 17 p. http://www.numdam.org/item/SEDP_2006-2007____A4_0/

[1] N. Anantharaman, Entropy and the localization of eigenfunctions, to appear in Ann. Math.

[2] N. Anantharaman, S. Nonnenmacher, Entropy of semiclassical measures of the Walsh-quantized baker’s map, to appear in Ann. H. Poincaré. | Zbl

[3] N. Anantharaman, S. Nonnenmacher, Half–delocalization of eigenfunctions of the laplacian on an Anosov manifold, | HAL

[4] M.V. Berry, Regular and irregular semiclassical wave functions, J.Phys. A 10, 2083–2091 (1977) | MR | Zbl

[5] O. Bohigas, Random matrix theory and chaotic dynamics, in M.J. Giannoni, A. Voros and J. Zinn-Justin eds., Chaos et physique quantique, (École d’été des Houches, Session LII, 1989), North Holland, 1991

[6] J. Bourgain, E. Lindenstrauss, Entropy of quantum limits, Comm. Math. Phys. 233, 153–171 (2003). | MR | Zbl

[7] A. Bouzouina and D. Robert: Uniform Semi-classical Estimates for the Propagation of Quantum Observables, Duke Math. J. 111, 223–252 (2002) | MR | Zbl

[8] Y. Colin de Verdière, Ergodicité et fonctions propres du laplacien, Commun. Math. Phys. 102, 497–502 (1985) | MR | Zbl

[9] A. Connes, H. Narnhofer, W. Thirring, Dynamical entropy of C * algebras and von Neumann algebras, Comm. Math. Phys. 112 no. 4, 691–719 (1987). | MR | Zbl

[10] M. Dimassi, J. Sjöstrand, Spectral asymptotics in the semi-classical limit, London Mathematical Society Lecture Note Series, 268. Cambridge University Press, Cambridge, 1999. | MR | Zbl

[11] L.C. Evans and M. Zworski, Lectures on semiclassical analysis (version 0.2), available at http://math.berkeley.edu/~zworski

[12] F. Faure, S. Nonnenmacher and S. De Bièvre, Scarred eigenstates for quantum cat maps of minimal periods, Commun. Math. Phys. 239, 449–492 (2003). | MR | Zbl

[13] F. Faure and S. Nonnenmacher, On the maximal scarring for quantum cat map eigenstates, Commun. Math. Phys. 245, 201–214 (2004) | MR | Zbl

[14] A. Katok and B. Hasselblatt, Introduction to the modern theory of dynamical systems, Encyclopedia of Mathematics and its applications vol.54, Cambridge University Press, 1995. | MR | Zbl

[15] D. Kelmer, Arithmetic quantum unique ergodicity for symplectic linear maps of the multidimensional torus, preprint (2005) math-ph/0510079

[16] K. Kraus, Complementary observables and uncertainty relations, Phys. Rev. D 35, 3070–3075 (1987) | MR

[17] P. Kurlberg and Z. Rudnick, Hecke theory and equidistribution for the quantization of linear maps of the torus, Duke Math. J. 103, 47–77 (2000) | MR | Zbl

[18] F. Ledrappier, L.-S. Young, The metric entropy of diffeomorphisms. I. Characterization of measures satisfying Pesin’s entropy formula, Ann. of Math. (2) 122 (1985), no. 3, 509–539. | Zbl

[19] E. Lindenstrauss, Invariant measures and arithmetic quantum unique ergodicity, Annals of Math. 163, 165-219 (2006) | MR | Zbl

[20] H. Maassen and J.B.M. Uffink, Generalized entropic uncertainty relations, Phys. Rev. Lett. 60, 1103–1106 (1988) | MR

[21] Z. Rudnick and P. Sarnak, The behaviour of eigenstates of arithmetic hyperbolic manifolds, Commun. Math. Phys. 161, 195–213 (1994) | MR | Zbl

[22] A. Schnirelman, Ergodic properties of eigenfunctions, Usp. Math. Nauk. 29, 181–182 (1974) | MR

[23] J. Sjöstrand and M. Zworski, Asymptotic distribution of resonances for convex obstacles, Acta Math. 183, 191–253 (1999) | MR | Zbl

[24] A. Voros, Semiclassical ergodicity of quantum eigenstates in the Wigner representation, Lect. Notes Phys. 93, 326-333 (1979) in: Stochastic Behavior in Classical and Quantum Hamiltonian Systems, G. Casati, J. Ford, eds., Proceedings of the Volta Memorial Conference, Como, Italy, 1977, Springer, Berlin | MR | Zbl

[25] S.A. Wolpert, The modulus of continuity for Γ 0 (m)/ semi-classical limits, Commun. Math. Phys. 216, 313–323 (2001) | MR | Zbl

[26] S. Zelditch, Uniform distribution of the eigenfunctions on compact hyperbolic surfaces, Duke Math. J. 55, 919–941 (1987) | MR | Zbl