Arbitrarily Fast Dispersion in Long Range Crystals

Mostafa Sabri (New York University Abu Dhabi)

Beyond Graph Laplacians

A dispersive estimate is a result of dynamical delocalization. It asserts that the supremum norm of wave packets decays like t^{-beta} as time goes on, under Schrodinger evolution. More precisely, || e^{itH} f||_infty \le t^{-beta} || f ||_1. A classical example is when H is the Laplacian on Z, where beta = 1/3. The fastest speed in one dimensional systems prior to our work was beta = 1/2, to the best of our knowledge.