Control for Schroedinger operators on tori

Nicolas Burq, Maciej Zworski

Published 2011-06-07Version 1

A well known result of Jaffard states that an arbitrary region on a torus controls, in the L2 sense, solutions of the free stationary and dynamical Schroedinger equations. In this note we show that the same result is valid in the presence of a smooth time-independent potential. The methods apply to continuous potentials as well and we conjecture that the L2 control is valid for any bounded time dependent potential.