Derivation of the transverse force on a moving vortex in a superfluid
D.J. Thouless, P. Ao, and Q. Niu
TL;DR
This paper provides an exact derivation of the nondissipative transverse force, specifically the Magnus force, acting on a moving vortex in a superfluid, applicable to both boson and fermion superfluids with a scalar order parameter.
Contribution
It offers a rigorous derivation of the transverse force on a vortex in superfluids, emphasizing the role of the one-particle density matrix and superfluid density.
Findings
The transverse force is the Magnus force proportional to superfluid density.
The derivation is valid for neutral boson and fermion superfluids with a scalar order parameter.
The force is determined by the one-particle density matrix far from the vortex core.
Abstract
We describe an exact derivation of the total nondissipative transverse force acting on a quantized vortex moving in a uniform background. The derivation is valid for neutral boson or fermion superfluids, provided the order parameter is a complex scalar quantity. The force is determined by the one-particle density matrix far away from the vortex core, and is found to be the Magnus force proportional to the superfluid density.
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