Topologically stable states of the geometric quantum potential

TL;DR

This paper explores how the geometric quantum potential on certain surfaces leads to topologically stable quantum states, using homotopy theory to estimate lower bounds and analyzing specific geometries like catenoids and tori.

Contribution

It introduces a novel approach by mapping the geometric quantum potential to the nonlinear sigma model and applying homotopy to estimate stability bounds.

Findings

Geometric quantum potential induces topologically stable states on various surfaces.

Homotopy theory provides a lower bound estimate for the quantum potential.

Specific geometries like catenoids and tori exhibit stable quantum states due to geometric effects.

Abstract

We map the geometric quantum potential on the nonlinear sigma model and use homotopy to estimate the lower bound of the geometric quantum potential. We investigate a catenoid (wormhole section), a two dimensional bilayer geometry smoothly connected by a neck and a torus to show that in all these cases the geometric quantum potential creates topologically stable quantum states.