2024/10/29 by Svetlana Jitomirskaya, Jitomirskaya, Svetlana, Wencai Liu +3 · 2 citations
Engineering · Computer Science · #Control Systems and Identification #Target Tracking and Data Fusion in Sensor Networks #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2410.21700
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.