Geometric Forces on Point Fluxes in Quantum Hall Fluids

TL;DR

This paper investigates the various forces acting on point fluxes in quantum Hall fluids, relating them to adiabatic curvature and analyzing differences between planar and toroidal geometries.

Contribution

It introduces a detailed analysis of forces on point fluxes in quantum Hall systems, connecting them to adiabatic curvature and geometric configurations.

Findings

Forces include external, Lorentz, Magnus, and mutual interactions.

Forces relate to adiabatic curvature of Landau Hamiltonians.

Differences between plane and torus geometries diminish at the thermodynamic limit.

Abstract

We study the forces that act on a point flux carrying an integral number of flux units in quantum Hall fluids. Forces due to external fields, Lorentz and Magnus type forces, and the forces due to mutual interaction of point fluxes are considered. The forces are related to the adiabatic curvature associated with families of Landau Hamiltonians. The problem displays distinct features of the quantum Hall fluids with point fluxes on the plane and on the torus, which, however, agree at the thermodynamic limit.