Tricritical Slowing Down of Superfluid Dynamics inHe3-He4Mixtures

Abstract

Measurements of the Rayleigh scattering by concentration fluctuations in the coexisting superfluid in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ mixtures near the tricritical temperature $T_t$ show a single Lorentzian line of width such that $\frac{\Gamma }{q^2}=D_{\mathrm{eff}}=1.5\mathrm{}\times {10}^{-4\mathrm{}}{\epsilon }^{0.95\pm 0.07}$ ${\mathrm{cm}}^2$ ${\sec }^{-1\mathrm{}}$ for $9\times {10}^{-4\mathrm{}}<~1-\frac{T}{T_t}\equiv \epsilon <~7\times {10}^{-3\mathrm{}}$. Thus the effective diffusion coefficient $D_{\mathrm{eff}}$ is proportional to ${\epsilon }^{+1\mathrm{}}$ and, since the concentration susceptibility ${\left(\frac{\partial x}{\partial \Delta }\right)}_{\mathrm{PT}}$ is proportional to ${\epsilon }^{-1\mathrm{}}$, the effective kinetic coefficient $L_{D,\mathrm{eff}}=\frac{D_{\mathrm{eff}}}{{\left(\frac{\partial \Delta }{\partial x}\right)}_{\mathrm{PT}}}$ is proportional to ${\epsilon }^{+1\mathrm{}}{\epsilon }^{-1\mathrm{}}\sim {\epsilon }^0$.