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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.

Keywords

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

R2 v1 2026-06-24T07:06:39.410Z