Seminar: Discrepancy Estimatesand Applications in Quantum Dynamics

Abstract: In this talk, we present new quantum dynamical upper bounds for one-dimensional analytic long-range operators with ergodic potentials, which improve over several previously known results. Our approach is based on novel discrepancy estimates for semi-algebraic sets. Specifically, for shift dynamics, we establish an asymptotically sharp discrepancy bound by constructing a matching lower bound. For skew-shift dynamics, we reduce the exponential upper bound to a polynomial one by Vinogradov's method.

Host: Xiang Tang