Effect of tunneling disorder on the low-temperature heat capacities of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ in zeolite channels

In an earlier work, interacting helium atoms confined inside K-L zeolite cages at low concentrations and low temperatures were assumed to tunnel between equivalent sites located near the cage wall. The corresponding Bose-Hubbard (for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$) and Mott-Hubbard (for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$) models yield heat capacities in reasonable agreement with experiments except at very low temperatures. Here we study the effect of disorder by extending the model by taking a random distribution of tunneling parameters, computing the energies and averaging the heat capacity using different probability distributions. This approach to a quantitative evaluation of the effects of disorder on the low-T heat-capacity yields results in much better agreement with experiment. © 1996 The American Physical Society.