Control for Schroedinger operators on tori
For mathematicians studying control theory of PDEs, this is an incremental extension of a known result to a slightly broader class of potentials.
The paper extends Jaffard's control result for the free Schrödinger equation on tori to include smooth time-independent potentials, showing that any region controls solutions in the L2 sense. The authors conjecture the result holds for bounded time-dependent potentials.
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.