Microscopic Theory of the Kapitza Resistance at a Solid-LiquidHe4Interface

We present the first completely quantum-mechanical calculation of the Kapitza resistance for the solid-liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ interface. By using a realistic model of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, processes involving phonons and rotons in the liquid helium are treated in a unified manner. The coupling of the phonons in the solid to the excitations in the helium is derived in the form of a transfer Hamiltonian. In the long-wavelength limit the classical acoustic-mismatch theory is reproduced by transmission processes involving single phonons, but the coupling Hamiltonian also includes roton emission and higher-order processes involving two or more excitations in the helium. As in the theory of electron tunneling, the transfer-Hamiltonian formalism can serve as a basis for further studies taking account of many-body interactions in the solid or liquid, scattering by defects or surface structure, and the influence of attractive van der Waals forces at the interface.