Statistical Physics, Second Revised and Enlarged Edition

162 Dealingwith interactions

The Landauparameters relate to other measuredquantities also,forinstance the
viscosity and diffusion coefficients in the liquid. These transport properties can be
explainedon Fermiliquidtheory witha remarkableefficiency andusing no new
assumptions. Theonlyadditionalidea tobeintroduced(andworkedout usingthe
theory) is that of the mean free pathlfor^3 He–^3 He scattering. Because of the Exclusion
Principle, scattering can onlytakeplacefor quasiparticles withenergies up to about
kkkBTfrom the Fermienergy.Thisleadstothe resultl ∝T−^2 inthedegenerate
FD regime, so that the mean free path, and with it the viscosity of the liquid, gets
extremely largeatlow temperatures. For example, theviscosityofpure^3 Hejust
above its superfluid transition at 1 mK is about the same as the engine oil in a car!
(See Fig. 1 5 .3 for some measurements related to this viscosity; the fluid thins out
dramaticallyagainwhenitbecomes a superfluid.)
Therefore we now have a veryfull understandingof the properties of liquid^3 He.
If that were the end of the Landau story, it would be clever, but not world-shattering.
However, thereis even more to relate. The reallysplendidthingisthat Landau’s
theorypredicted some entirelynew effects. The most important of these is calledzero
sound. Normal sound in a gas does not propagate when the mean free path becomes
large enough;abellcannotbeheardthrougha vacuum. Thedensitygradients of
the sound wave cannot be established when the scattering length becomes larger
than the soundwavelength. Howeverintheinteracting Fermiliquid, an entirely
new type ofcollisionless collective motion oftheliquid becomes possible, with
the restoring force deriving from the interactions. Thus as the temperature is low-
ered(toincreasel)orasthe soundfrequencyisraised(tolower the wavelength),
itisobservedthat the soundvelocityshifts (from around180 to 190 m s−^1 )and
there is also a large attenuation in the changeover regime, as normal (‘first’) sound

45 MHz

1 5 MHz

10 20 50

Temperature (mK)

2 5

187

189

Velocity (ms

-^1
)

191

193

195

100

Fig. 14.2The velocityof sound in liquid^3 He at millikelvin temperatures. The measurements show the
transition from first (normal) sound at high temperatures to zero sound at low temperatures.