Low temperature mobility of the liquid-solid interface of 4He

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Abstract
At a moving liquid-solid interface, heat and mass transports are closely coupled. We show that the overall interface mobility involves a combination of three surface Onsager coefficients with bulk thermal impedances that describe evacuation of heat in the bulk. At low temperature, only phonons survive in the two phases : we propose a dissipative mechanism based on Compton scattering of phonons by kinks and steps. The resulting mobility is ∼ T -4 for a simple kink, ∼ T-3 for a single step. We emphasize the role of coherent scattering in going from one kink to a finite kink density and ultimately to a continuous step. For an array of steps, new complications occur in calculating the interface mobility : we propose qualitative arguments that stress the important physical features, leaving however the problem largely open