Wärmeleitfähigkeit von 4 He in der Nähe des superfluiden Phasenübergangs in begrenzter Geometrie
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 not unique, which leads to one adjustable parameter. Good agreement with experiment is observed for both geometries at vapour pressure and predictions are made for the L dependence of the specific heat at T=T_lambda at higher pressures. The specific heat obeys finite size scaling, and scaling functions are derived. As all non-universal parameters that are needed for calculating the thermal conductivity are known either from the infinite system or from statics, the calculation of this quantity is done without any adjustable parameter. Good agreement with experiment is observed for cylindrical geometry at and above T_lambda. No suitable experiments have been done for plate geometry. Predictions for the L dependence at T=T_lambda are given. Because of the slow asymptotic behaviour that is already known from the bulk system the thermal conductivity does not obey finite size scaling in the experimentally accessible region. Over a wide range in L, however, approximate scaling with an effective, non-universal exponent is fulfilled. For both quantities the surface contributions are identified. In the region, where L is much larger than the correlation length, these are the leading deviations from bulk behaviour.
info:eu-repo/classification/ddc/530, Helium-4, Supraflüssiges Helium, Kritischer Punkt, Wärmeleitfähigkeit, Renomierungsgruppe, Physik, kritische Phänomene, finite-size Effekte
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