Liquid helium-4: a bose liquid? 163changes to the new modeofzero sound. Some experimentalresults showingthis
effect are shown in Fig. 14.2. The rich experimental data here is entirely as predicted
by Landau theory, andgives a striking confirmation ofthevalidity ofthewhole
approach.
Finally in this section, we can remark that there are many forms of Fermi liquid
availabletothe^3 He physicist andfor whichLandau theory gives a gooddescription.
Besidespure^3 He as afunction ofpressure (andhencedensity), thereisalso thewhole
topic of^3 He–^4 He solutions.At low temperatures (say, below 100 mK), these solutions
have remarkablysimple properties. The^4 He component ofthesolutionisthermally
dead. It is well below the superfluid transition temperature, so that it has already
reached its zero entropy ground state (see section 9.2, and in particular Fig. 9.6). Thus
allofthethermalactionbelongstothe^3 He component only. Natureiskindhere,inthat
there is a substantial solubilityrangeof^3 Hein^4 He, from zero upto a 6 .8% solution
(at zero pressure; the solubility goes up to about 9. 5 % at 10 bar). Therefore we have a
Fermiliquidwhose concentration canbe variedover a wide range. Experiment shows
that the heat capacity(and manyother properties) follow the idealgas model verywell
indeed, but with modified parameters as expected from the Landau methodology. For
example, theeffective mass ofa^3 He quasiparticlein a very dilute^3 He–^4 Hesolution
is about 2.3 times the bare^3 He mass. This enhancement comes dominantly from
interactionwiththe^4 Hebackgroundfor solutions withless than 1% concentration,
so thatitisindependent ofthe^3 He concentration.These solutions are abeautiful
example of the detail of FD statistics, since the transition from classical (MB) towards
quantum (FD)behaviour canbefollowedfrom wellabove to well below the Fermi
temperature. The Fermitemperature ofa 0.1% solutionisabout 27 mK, andvaries
as(concentration)^2 /^3 (see section 8.1.3), so there is a lot of measurable^3 He physics
between 100 mK and (say) 5 mK, achievable with a dilution refrigerator (which itself
operates on^3 He–^4 He solubility, as mentioned earlier in section 10.1.1).
1 4.3 Liquid helium-4: A Bose liquid?
Unlike theprevious two sections about Fermi liquids, this section will be short. This
is because there is no simple way of dealing with interactions in a Bose–Einstein
system. In the Fermi–Dirac case, theeffect ofthe ‘unfriendly’statisticsistokeep the
particles apart. This limits the scope of the interactions and allows Landau theoryto
be used. There is some reasonable separation between one particle and the ‘others’
whichdressittoform a quasiparticle, simply because those ‘others’are all indifferent
states. Hence the success of the quasiparticle idea. In the case of a degenerate BE
gas, thereisnosuchseparation. Infact, the‘friendly’ statistics encourage precisely
theopposite, andtheparticlesinthe Bose-Einstein condensation crowdinto the
ground state.
What wehave seeninthe experimentalsituation (section 9.2)isthat theliquid
doeshaveaphase transition,but one ofa markedly differentbehaviourfrom that