Unique Continuation Properties from One Time for Hyperbolic Schrödinger Equations

In this paper, we investigate properties of unique continuation for hyperbolic Schrödinger equations with time-dependent complex-valued electric fields and time-independent real magnetic fields. We show that positive masses inside of a bounded region at a single time propagate outside the region and prove gaussian lower bounds for the solutions, provided a suitable average in space-time cylinders is taken.