Quantum Dynamical Bounds for Quasi-Periodic Operators with Liouville Frequencies

2025/10/29 by Bradshaw, Matthew, de Jong, Titus, Liu, Wencai +3
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2510.25603

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 \nα\ with quantitative Green's function estimates adapted to the Liouville setting.

Citations

• Semi-algebraic discrepancy estimates for multi-frequency shift sequences with applications to quantum dynamics
• Quantum dynamical bounds for long-range operators with skew-shift potentials
• Sharp palindromic criterion for semi-uniform dynamical localization
• Upper bounds on quantum dynamics in arbitrary dimension
• Logarithmic quantum dynamical bounds for arithmetically defined ergodic Schrödinger operators with smooth potentials
• Fine dimensional properties of spectral measures
• Exponential Dynamical Localization: Criterion and Applications
• Large deviation estimates and Hölder regularity of the Lyapunov exponents for quasi-periodic Schrödinger cocycles
• Complex Cellular Structures
• Universal reflective-hierarchical structure of quasiperiodic eigenfunctions and sharp spectral transition in phase
• Quantitative continuity of singular continuous spectral measures and arithmetic criteria for quasiperiodic Schrödinger operators

Related

• Semi-algebraic discrepancy estimates for multi-frequency shift sequences with applications to quantum dynamics
• Green's function estimates for long-range quasi-periodic operators on ℤ^d and applications
• Quantitative continuity of singular continuous spectral measures and arithmetic criteria for quasiperiodic Schrödinger operators
• Quantum dynamical bounds for long-range operators with skew-shift potentials
• Logarithmic quantum dynamical bounds for arithmetically defined ergodic Schrödinger operators with smooth potentials