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Baym, Gordon; Beck, D H; Pethick, C J
Journal of low temperature physics, 02/2015, Letnik: 178, Številka: 3-4Journal Article
We report microscopic calculations of the thermal conductivity, diffusion constant, and thermal diffusion constant for classical solutions of \( reversible reaction \) He in superfluid \( pound sterling \) He at temperatures \(T \lesssim 0.6\) K, where phonons are the dominant excitations of the \( pound sterling \) He. We focus on solutions with \( reversible reaction \) He concentrations \(\lesssim \) \(10-3}\) , for which the main scattering mechanisms are phonon-phonon scattering via 3-phonon Landau and Beliaev processes, which maintain the phonons in a drifting equilibrium distribution, and the slower process of \( reversible reaction \) He-phonon scattering, which is crucial for determining the \( reversible reaction \) He distribution function in transport. We use the fact that the relative changes in the energy and momentum of a \( reversible reaction \) He atom in a collision with a phonon are small to derive a Fokker-Planck equation for the \( reversible reaction \) He distribution function, which we show has an analytical solution in terms of Sonine polynomials. We also calculate the corrections to the Fokker-Planck results for the transport coefficients.
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