Quantum Dynamical Bounds for Quasi-Periodic Operators with Liouville Frequencies

Abstract

We establish quantum dynamical upper bounds for quasi-periodic Schrödinger operators with Liouville frequencies. Our approach combines semi-algebraic discrepancy estimates for the Kronecker sequence $\{n\alpha \}$ with quantitative Green's function estimates adapted to the Liouville setting.

20 pages. comments welcome!