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Title: Bounds on eigenfunctions of quantum cat maps
Abstract We studyℓnorms ofℓ2-normalized eigenfunctions of quantum cat maps. For maps with short quantum periods (constructed by Bonechi and de Biévre in F Bonechi and S De Bièvre (2000,Communications in Mathematical Physics,211, 659–686)) we show that there exists a sequence of eigenfunctionsuwith u log N 1 / 2 . For general eigenfunctions we show the upper bound u log N 1 / 2 . Here the semiclassical parameter is h = 2 π N 1 . Our upper bound is analogous to the one proved by Bérard in P Bérard (1977,Mathematische Zeitschrift,155, 249-276) for compact Riemannian manifolds without conjugate points.  more » « less
Award ID(s):
1749858
PAR ID:
10542556
Author(s) / Creator(s):
;
Publisher / Repository:
IOP Science
Date Published:
Journal Name:
Physica Scripta
Volume:
98
Issue:
11
ISSN:
0031-8949
Page Range / eLocation ID:
115123
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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