Wärmeleitfähigkeit von 4 He in der Nähe des superfluiden Phasenübergangs in begrenzter Geometrie
type: CreativeWork
description: Below a temperature T_lambda of about 2°K 4He enters a superfluid state undergoing a 2nd order phase transition. For the infinite system very precise calculations based on renormalization group theory have been published. In most cases there is good agreement of the theoretical predictions with both experiment and computer simulation. This comparison confirms the main conclusions of renormalization group theory: universality and scaling. There are several discrepancies for finite systems. Especially it is still unknown, whether scaling is valid for finite systems. Only a few theoretical results exist about the dynamics of finite systems. These results are either restricted to surface effects or to non-physical periodic boundary conditions and systems with simple relaxational dynamics, which are not applicable to 4He. Experimental results of the thermal conductivity of 4He in cylindrical geometry have been published recently. Further experiments are planned for the near future. In this thesis renormalization group calculations for the dynamics of 4He in restricted geometry, with nonlinear boundary conditions for T>=T_lambda are presented for the first time. 3D Systems which are finite in one or two dimensions are considered. We assume Dirichlet boundary conditions for the order parameter density and Neumann boundary conditions for the entropy density. Whereas Dirichlet boundary conditions are established in static calculations, the entropy density is not needed in statics. Hydrodynamic arguments for the use of Neumann boundary conditions in dynamics are presented and it is shown, that these boundary conditions are consistent with the description of statics by the Landau-Ginzburg-Wilson functional. The calculation is done in first order of perturbation theory at fixed dimension d and infinite cutoff. Model F is used for the dynamical system. First, the specific heat is calculated for cylindrical and plate geometry for T>=T_lambda. The choice of the flow parameter is n…
abstract: Below a temperature T_lambda of about 2°K 4He enters a superfluid state undergoing a 2nd order phase transition. For the infinite system very precise calculations based on renormalization group theory have been published. In most cases there is good agreement of the theoretical predictions with both experiment and computer simulation. This comparison confirms the main conclusions of renormalization group theory: universality and scaling. There are several discrepancies for finite systems. Especially it is still unknown, whether scaling is valid for finite systems. Only a few theoretical results exist about the dynamics of finite systems. These results are either restricted to surface effects or to non-physical periodic boundary conditions and systems with simple relaxational dynamics, which are not applicable to 4He. Experimental results of the thermal conductivity of 4He in cylindrical geometry have been published recently. Further experiments are planned for the near future. In this thesis renormalization group calculations for the dynamics of 4He in restricted geometry, with nonlinear boundary conditions for T>=T_lambda are presented for the first time. 3D Systems which are finite in one or two dimensions are considered. We assume Dirichlet boundary conditions for the order parameter density and Neumann boundary conditions for the entropy density. Whereas Dirichlet boundary conditions are established in static calculations, the entropy density is not needed in statics. Hydrodynamic arguments for the use of Neumann boundary conditions in dynamics are presented and it is shown, that these boundary conditions are consistent with the description of statics by the Landau-Ginzburg-Wilson functional. The calculation is done in first order of perturbation theory at fixed dimension d and infinite cutoff. Model F is used for the dynamical system. First, the specific heat is calculated for cylindrical and plate geometry for T>=T_lambda. The choice of the flow parameter is n…
author: Töpler, Michael
language: ger
keywords: info:eu-repo/classification/ddc/530, Helium-4, Supraflüssiges Helium, Kritischer Punkt, Wärmeleitfähigkeit, Renomierungsgruppe, Physik, kritische Phänomene, finite-size Effekte
date published: 2004
date modified: 2026-07-30T19:43:28Z
provider: RWTH Aachen University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Publikationsserver der RWTH Aachen University