How heat propagates in liquid ${}^3$He

Abstract

In Landau's Fermi liquid picture, transport is governed by scattering between quasi-particles. The normal liquid ${}^3$He conforms to this picture but only at very low temperature. Here, we show that the deviation from the standard behavior is concomitant with the fermion-fermion scattering time falling below the Planckian time, $\frac{\hslash }{k_{\mathrm{B}}T}$ and the thermal diffusivity of this quantum liquid is bounded by a minimum set by fundamental physical constants and observed in classical liquids. This points to collective excitations (a sound mode) as carriers of heat. We propose that this mode has a wavevector of 2$k_F$ and a mean free path equal to the de Broglie thermal length. This would provide an additional conducting channel with a $T^{1/2}$ temperature dependence, matching what is observed by experiments. The experimental data from 0.007 K to 3 K can be accounted for, with a margin of 10\%, if thermal conductivity is the sum of two contributions: one by quasi-particles (varying as the inverse of temperature) and and another by sound (following the square root of temperature).

arXiv comment8 pages, 5 figures and a supplement

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Cited by in corpus (2)

• Electronic thermal resistivity and quasi-particle collision cross-section in semi-metals
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