Resonances for Open Quantum Maps and a Fractal Uncertainty Principle
Name
1608.02238.pdf
Description
Accepted version
Size
4.89 MB
Format
Adobe PDF
Checksum (MD5)
949cfde14c81200c626699d12859fc61
Author(s)
Dyatlov, Semyon
Jin, Long
Date Issued
2017
Journal
Communications in Mathematical Physics
Publisher
Springer Nature
Version
Author's final manuscript
Abstract
© 2017, Springer-Verlag Berlin Heidelberg. We study eigenvalues of quantum open baker’s maps with trapped sets given by linear arithmetic Cantor sets of dimensions δ∈ (0 , 1). We show that the size of the spectral gap is strictly greater than the standard bound max(0,12-δ) for all values of δ, which is the first result of this kind. The size of the improvement is determined from a fractal uncertainty principle and can be computed for any given Cantor set. We next show a fractal Weyl upper bound for the number of eigenvalues in annuli, with exponent which depends on the inner radius of the annulus.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/S00220-017-2892-Z
