Derivation of the Biot-Savart equation from the nonlinear Schrödinger equation

Miguel D. Bustamante and Sergey Nazarenko
Phys. Rev. E 92, 053019 – Published 25 November 2015
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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=κ28π|ss|>ξ*ds·ds|ss|,with cutoff length ξ*0.3416293/ρ0, where ρ0 is the background condensate density far from the vortex lines and κ is the quantum of circulation.

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  • Received 28 July 2015

DOI:https://doi.org/10.1103/PhysRevE.92.053019

©2015 American Physical Society

Authors & Affiliations

Miguel D. Bustamante*

  • Complex and Adaptive Systems Laboratory, School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland

Sergey Nazarenko

  • Mathematics Institute, The University of Warwick, Coventry, CV4 7AL, United Kingdom

  • *miguel.bustamante@ucd.ie
  • s.v.nazarenko@warwick.ac.uk

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Issue

Vol. 92, Iss. 5 — November 2015

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