http://arxiv.org/PS_cache/cond-mat/pdf/9512/9512175v1.pdf
Reference:
3.10 display: "This feature is similar to the vortex for bose fluid."
4. Summary
We have studied a possible occurence of the geometric force in a magnetic
condensate. This force is analogous to the Magnus force in ordinary superfluids.
The characteristic property is the nature of the â€transversalityâ€, so to speak, since
the force is perpendicular to the velocity of â€particle(vortex)â€, which suggests
that the force does not attribute to the energy dissipation. This feature is a
characteristics of the Lorentz force, so the geometric force is a sort of the Lorentz
force. However, it should be noted that the analogy with the Magnus force is
not complete, since in the magetic condensate we have no supercurrent as in the
case of the superfluids.
From the above derivation, the geometric force is attributed to the canonical
term, which arises from the geometric phase. From the formulation point of view,
the geometric force may be regarded as a special case of the pervious treatment
of the many vortex dynamics. However, the effective Lagrangian for the single
vortex can naturally incorporate the effect of pinning force, if we include the
interaction with the magnetic impurities immersed in the magnetic substance.
Indeed, we have shown that by using the Bohr-Sommerfeld quantization the
geometric force results in the bound state of a vortex which is captured by a
pinning potential. Apart from such a potential problem, the geomtric force would
play a role for an estimate of an effect of dynamical perturbation acting for the
vortex motion. The details of this will be given eleswhere.