Diffusive heat flow and sum rules in the hydrodynamic limit of normal 3He

Abstract

In earlier work it was shown that a sinusoidal distribution ~cos (αx) at time t = 0 will decay as α → 0, t→ ∞ with the excitation of damped, standing waves of first sound. To consider thermal conduction in a first-sound wave, we modify the solution of the Boltzmann equation by introducing a thermal diffusive pole into the Fourier time and space transform, in such a way that the f-sum and compressibility sum rules remain satisfied. The diffusivity factor D appearing in this pole is determined by the consistency condition that ∂2 T/ ∂t 2 calculated in two ways should give the same result. One of these ways proceeds by differentiation of an expression relating the temperature fluctuation δT to the quasiparticle momentum distribution, and the other approach utilizes the hydrodynamic equation of energy conservation. Elimination of D from the problem via this consistency condition makes possible an estimate of F 2 s = −2.65 for the Landau parameter, on application of the additional condition that the f-sum rule holds true to terms of fourth order in the wave vector. Use of this value in an expression derived for thermal conductivity λ gives λT = 39.2 ergs/sec cm, in good agreement with experiment.