How heat propagates in `non-Fermi liquid' $^3$He

In Landau's Fermi liquid, transport is governed by scattering between quasi-particles. The normal liquid $^3$He conforms to this picture, but only when T$< 0.02$ T$_F$. Here, we observe that the deviation from the standard behavior is concomitant with the fermion-fermion scattering time falling below the Planckian time, $\frac{\hbar}{k_BT}$. The thermal diffusivity of this quantum liquid is bounded by a minimum set by fundamental physical constants and earlier observed in classical liquids. This implies that collective excitations of the liquid (a sound mode) are carrying heat. We argue that if heat is carried by 2k$_F$ hydrodynamic sound mode, both the amplitude and the hitherto unexplained $T^{1/2}$ temperature dependence of thermal conductivity find an explanation with no other adjustable parameter.Comment: 7 pages, 4 figures and a supplemen