Semi-algebraic discrepancy estimates for multi-frequency shift sequences with applications to quantum dynamics
Wencai Liu, Matthew Powell, Yiding Max Tang, Xueyin Wang, Ruixiang Zhang, Justin Zhou
TL;DR
This paper develops precise semi-algebraic discrepancy estimates for multi-frequency shift sequences and applies these results to derive new bounds on the quantum dynamics of long-range quasi-periodic Schrödinger operators.
Contribution
It introduces sharp discrepancy estimates for multi-frequency sequences and applies them to improve bounds in quantum dynamical systems.
Findings
Sharp discrepancy estimates for multi-frequency sequences
New upper bounds for quantum dynamics of quasi-periodic Schrödinger operators
Enhanced understanding of long-range quantum systems
Abstract
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 of long-range quasi-periodic Schr\"odinger operators.
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