Parafluidity in helium near the λ-transition and the generalized time-dependent Landau theory

Abstract

A phenomenological theory of parafluidity, i.e., an enhancement of fluidity due to order-parameter fluctuations, is presented for helium near the λ transition. The generalized time-dependent Landau theory of second-order phase transitions is reviewed in general and is applied to the superfluid transition in helium as a particular example. In helium, it is found that parafluidity is manifested in the divergences of the mass diffusivity$D_m \propto \varepsilon ^{ - \tfrac{1}{3}}$, the thermal conductivity$\kappa \propto \varepsilon ^{ - \tfrac{1}{3}}$, the first-sound amplitude attenuation α ∝ |ε|⁻¹, and the second-sound dampling$D_2 \propto ( - \varepsilon )^{ - \tfrac{1}{3}}$, which are all consistent with the dynamic scaling hypothesis. Here a characteristic relaxation time τ ₀ ∝ |ε|⁻¹ is used, where ε=(T−T _c )/T _c andT _c is the transition temperature. Although there are not enough experimental data to confirm our formulas, the present approach is seen to agree in order of magnitude with available experiments. Finally, the sound absorption above a ferromagnetic transition is calculated by adding a diffusion term to the generalized time-dependent Landau equation. The result thus obtained agrees in order of magnitude with experiments in nickel.