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

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Title: Derivation of the Biot-Savart equation from the Nonlinear Schrödinger equation
Authors: Bustamante, Miguel
Nazarenko, Sergey
Permanent link: http://hdl.handle.net/10197/7282
Date: 25-Nov-2015
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, [equation not represented here], with cutoff length [equation not represented here], where ρ0 is the background condensate density far from the vortex lines and κ is the quantum of circulation.
Funding Details: Science Foundation Ireland
Type of material: Journal Article
Publisher: American Physical Society
Copyright (published version): 2015 American Physical Society
Keywords: Superfluid dynamics;Turbulence;Equations;Derivations
DOI: http://dx.doi.org/10.1103/PhysRevE.92.053019
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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