Temperature relaxation and the Kapitza boundary resistance paradox

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The calculation of the Kapitza boundary resistance between dissimilar harmonic solids has since long (Little [Can. J. Phys. 37, 334 (1959)]) suffered from a paradox: this resistance erroneously tends to a finite value in the limit of identical solids. We resolve this paradox by calculating temperature differences in the final heat-transporting state, rather than with respect to the initial state of local equilibrium. For a one-dimensional model we thus derive an exact, paradox-free formula for the boundary resistance. The analogy to ballistic electron transport is explained.
10 p., REVTeX 3.0 with LaTeX 2.09, ITFA-94-24

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Condensed Matter

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https://dspace.dare.co.zw/handle/123456789/38347

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arXiv

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