Rigorous and generalized derivation of vortex line dynamics in superfluids and superconductors
Journal
SIAM Journal on Applied Mathematics
Journal Volume
60
Journal Issue
3
Pages
1099-1110
Date Issued
2000
Author(s)
Lin, T.-C.
Abstract
We prove rigorously the asymptotic motion equation of a vortex line in a superconductor and a superfluid at small coherence length ε. In superconductors, the leading order term of the motion equation of a vortex line is dominated by the curvature and the normal direction of the vortex line. In superfluids, the leading order term of the motion equation of a vortex line is determined by the curvature and the binormal direction of the vortex line. Fortunately, the motion equation of a vortex line in a superfluid has the same leading order term as the motion equation of a vortex line in an incompressible fluid at high Reynolds numbers. The method of our proof is more rigorous and generalized than the formal asymptotic analysis in the dynamics of fluid dynamic vortices.
Type
journal article