Hardy Uncertainty Principle and unique continuation properties of   covariant Schrodinger flows
  We prove a logarithmic convexity result for exponentially weighted $L^2$-norms of solutions to electromagnetic Schr\"odinger equation, without needing to assume smallness of the magnetic potential. As a consequence, we can prove a unique continuation result in the style of the Hardy uncertainty principle, which generalizes the analogous theorems which have been recently proved by Escauriaza, Kenig, Ponce and Vega. 
Juan Antonio Barcelo, Luca Fanelli, Susana Gutierrez, Alberto Ruiz,   and Mari Cruz Vilela
math.AP