Quantum quasiballistic dynamics and thick point spectrum
Mathematical Physics
2019-03-27 v2 math.MP
Spectral Theory
Abstract
We obtain dynamical lower bounds for some self-adjoint operators with pure point spectrum in terms of the spacing properties of their eigenvalues. In particular, it is shown that for systems with thick point spectrum, typically in Baire's sense, the dynamics of each initial condition (with respect to some orthonormal bases of the space) presents a quasiballistic behaviour. We present explicit applications to some Schr\"odinger operators.
Cite
@article{arxiv.1808.00162,
title = {Quantum quasiballistic dynamics and thick point spectrum},
author = {Moacir Aloisio and Silas L. Carvalho and César R. de Oliveira},
journal= {arXiv preprint arXiv:1808.00162},
year = {2019}
}
Comments
17 pages, to appear in Letters in Mathematical Physics. Major changes following suggestions of the referees