Mass Propagation for Electromagnetic Schr\"odinger Evolutions

TL;DR

This paper establishes conditions under which positive mass in electromagnetic Schr"odinger equations propagates outside a bounded region, extending understanding of solution behavior with complex potentials.

Contribution

It proves Gaussian lower bounds for solutions under geometric conditions on the magnetic potential, a novel result in electromagnetic Schr"odinger evolution analysis.

Findings

Positive mass propagates outside bounded regions under certain conditions

Gaussian lower bounds are valid for solutions with complex potentials

Propagation depends on geometric conditions of the magnetic potential

Abstract

We investigate the validity of gaussian lower bounds for solutions to an electromagnetic Schr\"odinger equation with a bounded time-dependent complex electric potential and a time-independent vector magnetic potential. We prove that, if a suitable geometric condition is satisfied by the vector potential, then positive masses inside of a bounded region at a single time propagate outside the region, provided a suitable average in space-time cylinders is taken.