Abstract

We present our recent works on localization estimates for quantum dynamics described by time-dependent linear Schrödinger equations. Whereas the latter are known to lack strict light cones, we prove the existence of effective light cones, obtain explicit upper bounds on the maximal propagation speed of quantum information, and derive long-time decay estimates for the probability leakage away from the effective light cones. The results are based on a generic framework oflocalization theory for abstract Schrödinger equations. Based on joint works with I.M. Sigal, M. Lemm, J. Faupin, and others.