Local temperature measurement and Kapitza boundary resistance
Maassen van den Brink, A.
TNO Fysisch en Elektronisch Laboratorium
A calculation of the Kapitza boundary resistance between harmonic solids has been noted previously (Little, Can. J. Phys. 37 (1959) 334; Leung and Young, Phys. Rev. B 36 (1987) 4973) to lead to apparently paradoxical results in the limit of identical solids: instead of vanishing, the resistance tends to a finite limit. We resolve this paradox by calculating temperature differences in the final heat-transporting state of the system, i.e., not in the initial state of local equilibrium. For a quantum mechanical model of an interface between harmonic solids with temperature probes attached, exact calculations relate the probe temperatures to non-equilibrium energy densities. The analogy with two- and four-terminal resistance measurements in ballistic electron transport is also discussed.
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Physica B : Condensed Matter, 219-220 (1-4), 656-659