Statistical Physics, Second Revised and Enlarged Edition

Superfluid states in Fermi–Dirac systems 173

Temperature (mK)

Pressure

(b

ar

)

Normal liquid

0

0

10

20

30

40

123

Superfluiduperflui

B-phaseB-phase

Solid

A

Fig. 15.2Thephasediagram of^3 Heatmillikelvin temperatures, andin zero appliedmagneticfield.The
A-andB-phases aredifferent superfluidphases.

3 .Inthe A-phase, these vectors correspondtoaspin(S)direction andan orbital

(L)direction, sharedbyallpairsin a particular region ofthefluid. Hence the

A-phase has many similarities with liquid crystals, which also order with a highly

anisotropic vector orderingparameter. (Themagnitudeoftheorder parameter

gives the strength of the ordering; the direction of the vectorgives the direction

of alignment of the liquid crystal molecules.)

4. In the B-phase, theS=1,L= 1 pairs collect togetherin a muchmore uniform
   way, and the anisotropyis practicallynon-existent (although it can have secondary
   manifestations). Many experimental properties of the B-phase are described sim-
   ply in terms ofasingle scalarparameter. Figure 15.3gives an example of this
   type of behaviour, and it also serves as a dramatic illustration of the existence of
   superfluidity.As noted above in section 14.2.2,^3 Heisahighlyviscousliquidabove
   TTTC,so that thedampingofavibratingwireis verylarge. When theliquid is cooled
   belowTTTC, however, the damping falls off rapidly, varying as exp(−/kkkBT),the
   usualBoltzmannfactor, atlow temperatures as the normalfluid isfrozen out. At
   thelowest temperatures thevibratorbehaves asif in a vacuum withadamping
   coefficient 100 000 times less than atTTTC.


5. The fact that the pairs haveS= 1 means that they are magnetic. Thebehaviour
   ofthe superfluid isthus profoundly influencedbyappliedmagneticfields. This
   is so even in the B-phase, which becomes unstable if a large enough field (of
   order 0.4T)is applied,the superfluidreverting to the more magneticA-phase. The
   wholephasediagram changes, whichiswhytheB= 0 qualification was needed