Geodesic
On the distribution of matrix elements for the quantum cat map
Pär Kurlberg1 ; Zeév Rudnick2
1 Department of Mathematics, Royal Institute of Technology, 10044 Stockholm, Sweden
2 School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Annals of mathematics, Tome 161 (2005) no. 1, pp. 489-507.

Voir la notice de l'article provenant de la source Annals of Mathematics website

For many classically chaotic systems it is believed that the quantum wave functions become uniformly distributed, that is the matrix elements of smooth observables tend to the phase space average of the observable. In this paper we study the fluctuations of the matrix elements for the desymmetrized quantum cat map. We present a conjecture for the distribution of the normalized matrix elements, namely that their distribution is that of a certain weighted sum of traces of independent matrices in $\mathrm{SU}(2)$. This is in contrast to generic chaotic systems where the distribution is expected to be Gaussian. We compute the second and fourth moment of the normalized matrix elements and obtain agreement with our conjecture.
DOI : 10.4007/annals.2005.161.489

Pär Kurlberg 1 ; Zeév Rudnick 2

1 Department of Mathematics, Royal Institute of Technology, 10044 Stockholm, Sweden
2 School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel 
@article{10_4007_annals_2005_161_489,
     author = {P\"ar Kurlberg and Ze\'ev Rudnick},
     title = {On the distribution of matrix elements for the quantum cat map},
     journal = {Annals of mathematics},
     pages = {489--507},
     publisher = {mathdoc},
     volume = {161},
     number = {1},
     year = {2005},
     doi = {10.4007/annals.2005.161.489},
     mrnumber = {2150390},
     zbl = {1082.81054},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2005.161.489/}
}
TY  - JOUR
AU  - Pär Kurlberg
AU  - Zeév Rudnick
TI  - On the distribution of matrix elements for the quantum cat map
JO  - Annals of mathematics
PY  - 2005
SP  - 489
EP  - 507
VL  - 161
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2005.161.489/
DO  - 10.4007/annals.2005.161.489
LA  - en
ID  - 10_4007_annals_2005_161_489
ER  - 
%0 Journal Article
%A Pär Kurlberg
%A Zeév Rudnick
%T On the distribution of matrix elements for the quantum cat map
%J Annals of mathematics
%D 2005
%P 489-507
%V 161
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2005.161.489/
%R 10.4007/annals.2005.161.489
%G en
%F 10_4007_annals_2005_161_489
Pär Kurlberg; Zeév Rudnick. On the distribution of matrix elements for the quantum cat map. Annals of mathematics, Tome 161 (2005) no. 1, pp. 489-507. doi : 10.4007/annals.2005.161.489. http://geodesic.mathdoc.fr/articles/10.4007/annals.2005.161.489/

Cité par Sources :