title: Derivation of the Biot-Savart equation from the nonlinear Schrödinger equation.
abstract: We present a systematic derivation of the Biot-Savart equation from the nonlinear Schrödinger equation, in the limit when the curvature radius of vortex lines and the intervortex distance are much greater than the vortex healing length, or core radius. We derive the Biot-Savart equations in Hamiltonian form with Hamiltonian expressed in terms of vortex lines,H=κ(2)/8π∫(|s-s'|>ξ(*))(ds·ds')/|s-s'|,with cutoff length ξ(*)≈0.3416293/√(ρ(0)), where ρ(0) is the background condensate density far from the vortex lines and κ is the quantum of circulation.
authors.affiliation: Complex and Adaptive Systems Laboratory, School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland.
authors.forename: Miguel D
authors.initials: MD
authors.lastname: Bustamante
authors.affiliation: Mathematics Institute, The University of Warwick, Coventry, CV4 7AL, United Kingdom.
authors.forename: Sergey
authors.initials: S
authors.lastname: Nazarenko