Semifluxon degeneracy choreography in Aharonov-Bohm billiards

TL;DR

This paper investigates the degeneracy patterns of energy levels in a charged quantum particle system influenced by magnetic flux lines, revealing how shape and semifluxon positions affect degeneracies and deriving the forces involved.

Contribution

It introduces a detailed analysis of degeneracy choreography in Aharonov-Bohm billiards with semifluxons, including new computational methods and degeneracy conditions.

Findings

Degeneracies depend on the shape of the boundary and semifluxon positions.

Two degeneracies between the same levels can collide and annihilate.

The number of levels that can be degenerate is related to the number of semifluxons.

Abstract

Every energy level of a charged quantum particle confined in a region threaded by a magnetic flux line with quantum flux one-half must be degenerate for some position of the semifluxon within the boundary B. This is illustrated by computations for which B is a circle and a conformal transformation of a circle without symmetry. As the shape of B is varied, two degeneracies between the same pair of levels can collide and annihilate. Degeneracy of three levels requires three shape parameters, or the positions of three semifluxons; degeneracy of N levels can be generated by int{N(N+1)/4} semifluxons. The force on the semifluxon is derived.