Density Profile of a Quantized Vortex Line in Superfluid Helium-4

PDF Version Also Available for Download.

Description

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 ... continued below

Physical Description

viii, 174 leaves : ill.

Creation Information

Harper, John Howard May 1975.

Context

This dissertation is part of the collection entitled: UNT Theses and Dissertations and was provided by UNT Libraries to Digital Library, a digital repository hosted by the UNT Libraries. More information about this dissertation can be viewed below.

Who

People and organizations associated with either the creation of this dissertation or its content.

Publisher

Rights Holder

For guidance see Citations, Rights, Re-Use.

  • Harper, John Howard

Provided By

UNT Libraries

The UNT Libraries serve the university and community by providing access to physical and online collections, fostering information literacy, supporting academic research, and much, much more.

Contact Us

What

Descriptive information to help identify this dissertation. Follow the links below to find similar items on the Digital Library.

Degree Information

Description

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.

Physical Description

viii, 174 leaves : ill.

Subjects

Language

Identifier

Unique identifying numbers for this dissertation in the Digital Library or other systems.

Collections

This dissertation is part of the following collection of related materials.

UNT Theses and Dissertations

Theses and dissertations represent a wealth of scholarly and artistic content created by masters and doctoral students in the degree-seeking process. Some ETDs in this collection are restricted to use by the UNT community.

What responsibilities do I have when using this dissertation?

When

Dates and time periods associated with this dissertation.

Creation Date

  • May 1975

Added to The UNT Digital Library

  • March 9, 2015, 8:15 a.m.

Description Last Updated

  • May 9, 2019, 10:35 a.m.

Usage Statistics

When was this dissertation last used?

Yesterday: 0
Past 30 days: 2
Total Uses: 10

Interact With This Dissertation

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

International Image Interoperability Framework

IIF Logo

We support the IIIF Presentation API

Harper, John Howard. Density Profile of a Quantized Vortex Line in Superfluid Helium-4, dissertation, May 1975; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc500722/: accessed May 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .