Logarithmic quantum dynamical bounds for arithmetically defined ergodic Schr\"odinger operators with smooth potentials
Mathematical Physics
2021-10-25 v1 math.MP
Spectral Theory
Abstract
We present a method for obtaining power-logarithmic bounds on the growth of the moments of the position operator for one-dimensional ergodic Schr\"odinger operators. We use Bourgain's semi-algebraic method to obtain such bounds for operators with multifrequency shift or skew shift underlying dynamics with arithmetic conditions on the parameters.
Cite
@article{arxiv.2110.11883,
title = {Logarithmic quantum dynamical bounds for arithmetically defined ergodic Schr\"odinger operators with smooth potentials},
author = {Svetlana Jitomirskaya and Matthew Powell},
journal= {arXiv preprint arXiv:2110.11883},
year = {2021}
}
Comments
26 pages