CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  Publicationsjournals
Publications        
Search results

Search: All articles in the CMB digital archive with keyword quantum limits

  Expand all        Collapse all Results 1 - 3 of 3

1. CMB 2013 (vol 56 pp. 827)

Petridis, Yiannis N.; Raulf, Nicole; Risager, Morten S.
Erratum to ``Quantum Limits of Eisenstein Series and Scattering States''
This paper provides an erratum to Y. N. Petridis, N. Raulf, and M. S. Risager, ``Quantum Limits of Eisenstein Series and Scattering States.'' Canad. Math. Bull., published online 2012-02-03, http://dx.doi.org/10.4153/CMB-2011-200-2.

Keywords:quantum limits, Eisenstein series, scattering poles
Categories:11F72, 8G25, 35P25

2. CMB 2012 (vol 56 pp. 814)

Petridis, Yiannis N.; Raulf, Nicole; Risager, Morten S.
Quantum Limits of Eisenstein Series and Scattering States
We identify the quantum limits of scattering states for the modular surface. This is obtained through the study of quantum measures of non-holomorphic Eisenstein series away from the critical line. We provide a range of stability for the quantum unique ergodicity theorem of Luo and Sarnak.

Keywords:quantum limits, Eisenstein series, scattering poles
Categories:11F72, 58G25, 35P25

3. CMB 2011 (vol 56 pp. 3)

Aïssiou, Tayeb
Semiclassical Limits of Eigenfunctions on Flat $n$-Dimensional Tori
We provide a proof of a conjecture by Jakobson, Nadirashvili, and Toth stating that on an $n$-dimensional flat torus $\mathbb T^{n}$, and the Fourier transform of squares of the eigenfunctions $|\varphi_\lambda|^2$ of the Laplacian have uniform $l^n$ bounds that do not depend on the eigenvalue $\lambda$. The proof is a generalization of an argument by Jakobson, et al. for the lower dimensional cases. These results imply uniform bounds for semiclassical limits on $\mathbb T^{n+2}$. We also prove a geometric lemma that bounds the number of codimension-one simplices satisfying a certain restriction on an $n$-dimensional sphere $S^n(\lambda)$ of radius $\sqrt{\lambda}$, and we use it in the proof.

Keywords:semiclassical limits, eigenfunctions of Laplacian on a torus, quantum limits
Categories:58G25, 81Q50, 35P20, 42B05

© Canadian Mathematical Society, 2014 : http://www.cms.math.ca/