Density Profile of a Quantized Vortex Line in Superfluid Helium-4
per
Harper, John Howard
Major Professor
per
Kobe, Donald Holm
Minor professor
per
Gray, Thomas James, 1917-
per
Deering, William D.
per
McIntyre, Bernard
per
Krishnan, Raj Muthu
www.unt.edu
Denton, Texas
North Texas State University
1975-05
eng
The density amplitude of an isolated quantum vortex line in superfluid 4He is calculated using a generalized Gross-Pitaevskii (G-P) equation. The generalized G-P equation for the order parameter extends the usual mean-field approach by replacing the interatomic potential in the ordinary G-P equation by a local, static T matrix, which takes correlations between the particles into account. The T matrix is a sum of ladder diagrams appearing in a diagrammatic expansion of the mean field term in an exact equation for the order parameter. It is an effective interaction which is much softer than the realistic interatomic Morse dipole-dipole potential from which it is calculated. A numerical solution of the generalized G-P equation is required since it is a nonlinear integro-differential equation with infinite limits. For the energy denominator in the T matrix equation, a free-particle spectrum and the observed phonon-roton spectrum are each used. For the fraction of particles in the zero-momentum state (Bose-Einstein dondensate) which enters the equation, both a theoretical value of 0.1 and an experimental value of 0.024 are used. The chemical potential is adjusted so that the density as a function of distance from the vortex core approaches the bulk density asymptotically. Solutions of the generalized G-P equation are not very dependent on the choice of energy denominator or condensate fraction. The density profile is a monotonically increasing function of the distance from the vortex core. The core radius, defined to be the distance to half the bulk density, varies from 3.7 A to 4.7 A, which is over three times the experimental value of 1.14 A at absolute zero.
viii, 174 leaves : ill.
density amplitudes
quantum vortex lines
Gross-Pitaevskii equation
Liquid helium.
Vortex-motion.
UNTETD
UNT
public
Harper, John Howard
copyright
Copyright is held by the author, unless otherwise noted. All rights reserved.
text_etd
text
379 N81d no.920
1843008
b1077370
1002784370-Harper
Doctoral
Physics Department
Physics
Doctor of Philosophy
disse
North Texas State University
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