Geometric phase related to point-interaction transport on a magnetic Lobachevsky plane

TL;DR

This paper investigates the geometric phase acquired by a charged quantum particle on a Lobachevsky plane due to adiabatic transport of a point interaction in a magnetic field, revealing a Berry phase proportional to the enclosed flux.

Contribution

It demonstrates a direct relation between the Berry phase and the magnetic flux for a quantum particle on a hyperbolic plane with a moving point interaction.

Findings

Berry phase equals 2π times the number of flux quanta

The phase depends on the area enclosed by the point interaction path

Results extend geometric phase concepts to hyperbolic geometries

Abstract

We consider a charged quantum particle living in the Lobachevsky plane and interacting with a homogeneous magnetic field perpendicular to the plane and a point interaction which is transported adiabatically along a closed loop C in the plane. We show that the bound-state eigenfunction acquires at that the Berry phase equal to 2\pi times the number of the flux quanta through the area encircled by C.