Topologically Stable States of the Anti-Centrifugal Potential

We present a study of the anti-centrifugal potential based on the incorporation of the quantum geometric potential of a surface [1] into the generalised anti-centrifugal potential [2]. As a basic variable we will use the unit normal to the surface. Then the total quantum effective potential appears to be the nonlinear sigma model plus positive terms. A 2d bilayer geometry smoothly connected by a neck is used to show that the anti-centrifugal potential creates topologically stable states.