A sharper discrepancy bound for multi-frequency shift sequences is derived and applied to quantum dynamics, but the supporting lower-bound proof counts points outside the allowed window.
Sharp palindromic criterion for semi-uniform dynamical localization
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abstract
We develop a sharp palindromic argument for general 1D operators, that proves absence of semi-uniform localization in the regime of exponential symmetry-based resonances. This provides the first examples of operators with dynamical localization but no SULE/SUDL, as well as with nearly uniform distribution of centers of localization in absence of SULE. For the almost Mathieu operators, this also leads to a sharp arithmetic criterion for semi-uniformity of dynamical localization in the Diophantine case.
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Semi-algebraic discrepancy estimates for multi-frequency shift sequences with applications to quantum dynamics
A sharper discrepancy bound for multi-frequency shift sequences is derived and applied to quantum dynamics, but the supporting lower-bound proof counts points outside the allowed window.