Interf\'erences pour les chats quantiques
General Mathematics
2026-01-15 v2
Abstract
In this text I study quantum dynamics of quantized linear automorphisms of the torus after the Ehrenfest time. I show that, in the wave packet basis, the 'matrix' of the associated propagator is well approximated by Birkhoff sums of nilrotations on the torus. In the second part, I conduct a thorough study of these sums and relate the equidistribution of evolved wave packets to a problem of Diophantine approximation.
Cite
@article{arxiv.2501.06190,
title = {Interf\'erences pour les chats quantiques},
author = {Jean-Michel Pipeau},
journal= {arXiv preprint arXiv:2501.06190},
year = {2026}
}
Comments
Master's thesis, in French, comments welcome, in any language. In this second version, we add a study of the Birkhoff sums. 85 pages 4 figures