Critical and tricritical dynamics in /sup 3/He--/sup 4/He mixtures

Journal Article · Sat Oct 01 04:00:00 EDT 1983 · J. Low Temp. Phys.; (United States)

DOI:https://doi.org/10.1007/BF00685780· OSTI ID:5652318

Onuki, A

A new formalism is presented to study the critical and tricritical dynamics of /sup 3/He--/sup 4/He mixtures near the superfluid transition for arbitrary concentration. In this fluid tow conserved variables, the molar concentration X and the entropy s, are twofold coupled to a complex order parameter phi first in the dynamic equations reversibly and second in the free energy dissipatively. However, at an intermediate concentration X = X/sub p/ (which is 0.37 at the saturated vapor pressure) a linear combination of X and s is found to be asymptotically decoupled from phi both reversibly and dissipatively. There, dynamic renormalization group equations reduce to those of pure /sup 4/He (or those of the F model) and some dynamic properties are common to those of pure /sup 4/He. For example, at Xapprox. =X/sub D/, the gradient del(T-T/sub lambda/) under heat flow goes to zero without /sup 3/He mass flow, where T/sub lambda/ is the critical temperature, dependent on X, and the thermodiffusion ratio loses the singularity with the critical exponent ..cap alpha... Our dynamic renormalization group equations take into account the above two nonlinear couplings and can be used for any concnetrations. Furthermore, using a linear response scheme, general relations are obtained among the kinetic coefficients. As a result the thermal conductivity on the lambda line is found to be exactly proportional to X/sup -1/ at small X. The coefficient in front of X/sup -1/ can be expressed in terms of the diffusion constant of an isolated /sup 3/He molecule in /sup 3/He.

• Research Organization: Research Institute for Fundamental Physics, Kyoto University, Kyoto, Japan
• OSTI ID: 5652318
• Journal Information: J. Low Temp. Phys.; (United States), Journal Name: J. Low Temp. Phys.; (United States) Vol. 53:1; ISSN JLTPA
• Country of Publication: United States
• Language: English

Related Subjects

640450* -- Fluid Physics-- Superfluidity
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
COLLECTIVE EXCITATIONS
DISPERSIONS
DYNAMICS
ENERGY-LEVEL TRANSITIONS
ENTROPY
EQUATIONS
EVEN-EVEN NUCLEI
EVEN-ODD NUCLEI
EXCITATION
FUNCTIONS
GINZBURG-LANDAU THEORY
GROUP THEORY
HELIUM 3
HELIUM 4
HELIUM ISOTOPES
ISOTOPES
KINETIC EQUATIONS
LIGHT NUCLEI
MATHEMATICS
MECHANICS
MIXTURES
NONLINEAR PROBLEMS
NUCLEI
ORDER PARAMETERS
PHYSICAL PROPERTIES
QUANTITY RATIO
RENORMALIZATION
RESPONSE FUNCTIONS
STABLE ISOTOPES
SUPERFLUIDITY
THERMODYNAMIC PROPERTIES