Logarithmic quantum dynamical bounds for arithmetically defined ergodic Schrödinger operators with smooth potentials

2021/10/22 by Svetlana Jitomirskaya, Matthew Powell, Jitomirskaya, Svetlana +1 · 2 citations
Mathematics · #Advanced Mathematical Physics Problems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2110.11883

openalex publication_date 2021/10/22 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We present a method for obtaining power-logarithmic bounds on the growth of the moments of the position operator for one-dimensional ergodic Schrödinger 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.

Cited by

• Quantum Dynamical Bounds for Quasi-Periodic Operators with Liouville Frequencies
• Semi-algebraic discrepancy estimates for multi-frequency shift sequences with applications to quantum dynamics

Related

• Quantum dynamical bounds for long-range operators with skew-shift potentials
• Upper bounds on quantum dynamics in arbitrary dimension
• Quantum Dynamical Bounds for Quasi-Periodic Operators with Liouville Frequencies
• Schrödinger operators with dynamically defined potentials
• Upper bounds in non-autonomous quantum dynamics