6 papers
Sharp Logarithmic Quantum Dynamics for Quasiperiodic Schrödinger Operators
Wencai Liu, Xueyin Wang
Dynamical localization requires all position moments of a quantum wavepacket to remain bounded in time, but for quasiperiodic Schrödinger operators such bounds are generally not un…
Primitive inhomogeneous approximation for fixed non-singular frequencies
Xueyin Wang
We prove a high-dimensional primitive inhomogeneous Diophantine approximation result for fixed non-singular simultaneous frequencies. The frequency class is explicit and has full L…
Continuity of Lyapunov Exponent for Quasi-Periodic Gevrey Cocycles
Xueyin Wang
It is shown that for the quasi-periodic cocycles in Gevrey space and subexponential Brjuno class frequency , the Lyapunov exponent is continuous provided that $1<s+η<…
Quantum Dynamical Bounds for Quasi-Periodic Operators with Liouville Frequencies
Matthew Bradshaw, Titus de Jong, Wencai Liu +3
We establish quantum dynamical upper bounds for quasi-periodic Schrödinger operators with Liouville frequencies. Our approach combines semi-algebraic discrepancy estimates for the…
Semi-algebraic discrepancy estimates for multi-frequency shift sequences with applications to quantum dynamics
Wencai Liu, Matthew Powell, Yiding Max Tang +3
We establish asymptotically sharp semi-algebraic discrepancy estimates for multi-frequency shift sequences. As an application, we obtain novel upper bounds for the quantum dynamics…
Quantum dynamical bounds for long-range operators with skew-shift potentials
Wencai Liu, Matthew Powell, Xueyin Wang
We employ Weyl's method and Vinogradov's method to analyze skew-shift dynamics on semi-algebraic sets. Consequently, we improve the quantum dynamical upper bounds of Jitomirskaya-P…