Diffusive heat flow and sum rules in the hydrodynamic limit of normal3He

✍ Scribed by R. E. Nettleton

• Publisher: Springer US
• Year: 1978
• Tongue: English
• Weight: 465 KB
• Volume: 31
• Category: Article
• ISSN: 0022-2291
• DOI: 10.1007/bf00115103

✦ Synopsis

In earlier work it was shown that a sinusoidal distribution -cos (ax) at time t = 0 will decay as a --> O, t-~ oo 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 32T/Ot e calculated in two ways should give the same result. One of these ways proceeds by differentiation of an expression relating the temperature fluctuation o~ 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 =-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 h gives AT = 39.2 ergs/sec cm, in good agreement with experiment.