Summary: Journal of Statistical Physics, Vol. 92, Nos. 5/6, 1998
Geometric Forces on Point Fluxes in
Quantum Hall Fluids
J. E. Avron1 and P. G. Zograf2
Received February 8, 1998
The forces that act on a point flux carrying an integral number of flux units in
quantum Hall fluids are related to the adiabatic curvature associated with
families of Landau Hamiltonians. We calculate the forces due to external fields,
Lorentz and Magnus forces, and the forces due to mutual interaction of point
fluxes.The forces are different for the plane and the torus, but agree at the ther-
modynamic limit of large tori.
A point flux in two dimensions is the magnetic analog of a point charge.
It is created by an (infmitesimally thin) Aharonov-Bohm flux tube that
orthogonally pierces the two dimensional surface in question. For reasons
that shall become clear later, we restrict ourselves to cases where the flux
0 is an integer multiple of the quantum flux unit 0 = hc/e.
A point flux in vacuum does not interact directly with electric or mag-
netic fields, nor with other point fluxes (by the linearity of Maxwell equa-
tions). However, point fluxes associated with, say, a two dimensional quan-
tum Hall fluid can interact through the electrons that fill the Landau level.