Flux String in Quantum Billiards with Two Particles

TL;DR

This paper studies the quantum behavior of two interacting particles in confined geometries, revealing phenomena like Berry phase and flux effects, and reduces complex multi-particle systems to effective one-particle models with flux strings.

Contribution

It introduces a novel reduction of two-particle quantum billiards with mass disparity to effective one-particle models involving flux strings, highlighting Berry phase effects.

Findings

Identification of Berry phase and magnetic flux in the system

Reduction to Aharonov-Bohm billiard in 2D

Effective flux string model in 3D

Abstract

We examine the quantum motion of two particles interacting through a contact force which are confined in a rectangular domain in two and three dimensions. When there is a difference in the mass scale of two particles, adiabatic separation of the fast and slow variables can be performed. Appearance of the Berry phase and magnetic flux is pointed out. The system is reduced to a one-particle Aharonov-Bohm billiard in two-dimensional case. In three dimension, the problem effectively becomes the motion of a particle in the presence of closed flux string in a box billiard.