Anomalous Thermal Conductivity in Very Dilute ³He-⁴He Solutions

Abstract

The measurements of Meyer’s group¹ at Duke University have revealed an unexpected deviation from Khalatnikov’s theory of very dilute ³He-⁴He solutions. The theoretical prediction is that K _eff , the effective thermal conductivity in the superfluid phase, should diverge as the reciprocal of the X, ³He mole fraction. In contrast, Meyer and coworkers have found K _eff leveling off at a finite value and apparently becoming nearly independent of X. This finding was corroborated by one measurement by Lipa and Chui at the very low value of X = 10⁻⁷. We have been able to account phenomenologically for this extremely puzzling behavior by means of a “3-fluid model,” which postulates that there is an additional normal component that interacts both with the ³He and with the gas of excitations in the liquid ⁴He (i.e., with the usual normal component). By fitting the parameters to the observed plateau, the 3-fluid model predicts that K _eff should rise again for even lower concentrations, in the range X < 10⁻⁷. Although difficult, this test ought to be feasible with the advanced thermometric techniques that are now available. The search for the predicted rise at X < 10⁻⁷ and the development of “quasi-Khalatnikov” behavior at the ultra-low concentrations will be a crucial test for the 3-fluid hypothesis.