Geometry induced potential on a 2D-section of a wormhole: catenoid

TL;DR

This paper demonstrates that a 2D wormhole geometry, modeled as a catenoid, induces a geometric potential affecting quantum states, with potential realizations in graphene, lattice dislocations, and nanoscale waveguides.

Contribution

It establishes the equivalence between a 2D wormhole and a catenoid surface and derives the resulting geometric potential and bound states for quantum particles.

Findings

Ground state corresponds to a reflectionless potential.

Bound states are obtained for various angular momentum channels.

Potential realizations include bent graphene sheets and nanoscale waveguides.

Abstract

We show that a two dimensional wormhole geometry is equivalent to a catenoid, a minimal surface. We then obtain the curvature induced geometric potential and show that the ground state with zero energy corresponds to a reflectionless potential. By introducing an appropriate coordinate system we also obtain bound states for different angular momentum channels. Our findings can be realized in suitably bent bilayer graphene sheets with a neck or in a honeycomb lattice with an array of dislocations or in nanoscale waveguides in the shape of a catenoid.