Critical dynamics near the lambda transition in /sup 3/He-/sup 4/He mixtures

Journal Article · Mon Aug 01 00:00:00 EDT 1983 · Phys. Rev. B: Condens. Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.28.1332· OSTI ID:5603576

Dohm, V; Folk, R

The critical dynamics of the lambda transition in /sup 3/He-/sup 4/He mixtures are studied by means of renormalized field theory applied to the model of Siggia and Nelson. A diagonal representation for the equations of motion is introduced, which greatly simplifies the computations in two-loop order. A universal connection is found with the asymptotic critical dynamics of pure /sup 4/He in all orders of perturbation theory. The observable critical dynamics of helium mixtures are dominated by nonuniversal crossover effects which can be properly described only within a nonlinear renormalization-group approach. The theory is applied to explain the observable critical and precritical temperature dependence of the mass diffusion D, of the thermal conductivity kappa, of the thermal diffusion ratio k/sub T/, and of the dynamic structure factor for T> or =T/sub lambda/(X). Recent experimental data for the transport coefficients at the molar /sup 3/He concentration X = 0.05 by Gestrich and Meyer are used to identify the nonuniversal parameters of the theory in the range X<<1. Consistency with the dynamics of pure /sup 4/He (X = 0) is verified. Predictions without adjustable parameters are made for the dynamic structure factor and the transport coefficients in very dilute mixtures. The Siggia-Kawasaki problem concerning the leading X dependence of kappa(T/sub lambda/) in the X..-->..0 limit is resolved. It is demonstrated that Siggia's prediction kappa(T/sub lambda/)approx.X/sup -1/ is correct but not observable. Theoretical extrapolations to X>0.05 without adjustable parameters are presented and compared with measured transport coefficients at X = 0.11 and 0.15. The overall agreement is satisfactory. Deviations of order 15% exist with the thermal conductivity kappa at X = 0.15. This may be attributed to dynamic effects arising from the singular specific heat and mass susceptibility, which are not included in the present analysis.

• Research Organization: Institut fuer Festkoerperforschung, Kernforschungsanlage Juelich, D-5170 Juelich, Germany
• OSTI ID: 5603576
• Journal Information: Phys. Rev. B: Condens. Matter; (United States), Vol. 28:3
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
HELIUM 3
SUPERFLUIDITY
HELIUM 4
LAMBDA POINT
MASS TRANSFER
MIXTURES
QUANTUM FIELD THEORY
RENORMALIZATION
STRUCTURE FACTORS
THERMAL CONDUCTIVITY
DISPERSIONS
EVEN-EVEN NUCLEI
EVEN-ODD NUCLEI
FIELD THEORIES
HELIUM ISOTOPES
ISOTOPES
LIGHT NUCLEI
NUCLEI
PHYSICAL PROPERTIES
STABLE ISOTOPES
THERMODYNAMIC PROPERTIES
TRANSITION TEMPERATURE
640450* - Fluid Physics- Superfluidity