A dynamical Amrein-Berthier uncertainty principle

Given a selfadjoint magnetic Schrödinger operator (Formula presented.) on L2(Rn), with V(x) strictly subquadratic and A(x) strictly sublinear, we prove that the flow u(t)=e-itHu(0) satisfies an Amrein–Berthier type inequality (Formula presented.) for all compact sets E,F⊂Rn. In particular, if both u(0) and u(T) are compactly supported, then u vanishes identically. Under different assumptions on the operator, which allow for time–dependent coefficients, the result extends to sets E, F of finite measure. We also consider a few variants for Schrödinger operators with singular coefficients, metaplectic operators, and we include applications to control theory.