On the scarring of eigenstates in some arithmetic hyperbolic manifolds

Abstract : In this paper, we deal with the conjecture of 'Quantum Unique Ergodicity'. Z. Rudnick and P. Sarnak showed that there is no 'strong scarring' on closed geodesics for arithmetic congruence surfaces derived from a quaternion division algebra. We extend this result to a class of three-dimensional Riemannian manifolds X=Gamma\H^3 that are again derived from quaternion division algebras. We show that there is no 'strong scarring' on closed geodesics or on Gamma-closed imbedded totally geodesics surfaces of X.
Type de document :
Pré-publication, Document de travail
Written in January-February 2003 and corrected in March 2004 and August 2005. 35 pages. 2005
Liste complète des métadonnées

Littérature citée [9 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00001491
Contributeur : Tristan Poullaouec <>
Soumis le : jeudi 8 décembre 2005 - 14:27:14
Dernière modification le : mardi 30 mai 2017 - 01:07:54
Document(s) archivé(s) le : vendredi 24 septembre 2010 - 10:25:13

Identifiants

Collections

Citation

Tristan Poullaouec. On the scarring of eigenstates in some arithmetic hyperbolic manifolds. Written in January-February 2003 and corrected in March 2004 and August 2005. 35 pages. 2005. 〈hal-00001491v4〉

Partager

Métriques

Consultations de la notice

119

Téléchargements de fichiers

115