KAPITZA CONDUCTANCE, TEMPERATURE-GRADIENTS, AND SOLUTIONS TO BOLTZMANN-EQUATION
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In the belief that the study of heat transport requires the study of the transport equation, we present an approach to the problem of the Kapitza conductance hK between two materials which involves the solutions of the Boltzmann equation. One of our purposes is to investigate the origin of the apparent temperature discontinuity T that is associated with this phenomenon. The hydrodynamic solutions of the Boltzmann equation, which (by definition) are describable in terms of local thermohydrodynamic variables, can transfer heat but are not at all responsible for T; whereas the nonhydrodynamic solutions are completely responsible for T but do not transfer heat. An effective temperature T is defined which approaches the thermodynamic temperature T far from the interface, and which is assumed to be continuous across the interface. With this assumption, formal expressions for T and hK are derived. In the limit as the properties of the two materials become identical, RK (=hK-1) approaches zero, as should be the case. Further, this approach has a natural generalization to finite frequencies and includes lifetime effects. It is pointed out that thermometers do not measure T but rather TR which reflects, in a complicated fashion, the presence of the nonhydrodynamic modes, whose amplitudes fall off exponentially as one moves from the interface. In He II, determination of the exponential damping lengths (as a function of temperature and pressure) would provide information about phonon dispersion and phonon interactions which is at least as detailed as could be obtained by other means. 1975 The American Physical Society.
