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

نویسندگان

  • Miguel D Bustamante
  • Sergey Nazarenko
چکیده

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.

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عنوان ژورنال:
  • Physical review. E, Statistical, nonlinear, and soft matter physics

دوره 92 5  شماره 

صفحات  -

تاریخ انتشار 2015