Temperature relaxation and the Kapitza boundary resistance paradox

Details Temperature relaxation and the Kapitza boundary resistance paradox Temperature relaxation and the Kapitza boundary resistance paradox

1994-07-28

arxiv.org/abs/cond-mat/9407113v1

Physics

Condensed Matter

10 p., REVTeX 3.0 with LaTeX 2.09, ITFA-94-24

Scientific paper

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.

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