Some lower bounds for solutions of Schrodinger evolutions

TL;DR

This paper establishes lower bounds for regular solutions of Schrödinger equations with bounded, time-dependent complex potentials, showing that initial mass within a region can be detected outside that region over time.

Contribution

It provides new lower bounds for solutions of Schrödinger equations with bounded, time-dependent potentials, linking initial mass to observable regions over time.

Findings

Initial mass within a ball can be observed outside that region over time.

Lower bounds depend on initial mass and properties of the potential.

Results apply to solutions with positive initial mass.

Abstract

We present some lower bounds for regular solutions of Schr\"odinger equations with bounded and time dependent complex potentials. Assuming that the solution has some positive mass at time zero within a ball of certain radius, we prove that this mass can be observed if one looks at the solution and its gradient in space-time regions outside of that ball.