174 Statistics under extreme conditions
Inverse temperature (1/TTT,T in mmmK)Log(d
amping) Normal
fluid00.00 00.1101000620Superfluiduperflui
B-phaseB-phaseTTTcFig. 15. 3 Thedamping ofavibrating wireinliquid^3 He, measuredbythe author andcolleaguesin
Lancaster. Thedamping changesbyaboutfive orders ofmagnitudefrom the transitiondown to thelowest
temperature (130μKinthis work). Thedampingisplottedlogarithmically against 1 /T,andthelinear
relationinthe superfluidshows that thedampingisfrozen outbythe gap Boltzmannfactor, exp(−/kkkBT).
in Fig. 15.2. In contrast with superconductors, the effect of the field onTTTCitself
is minor, but it reinforces one phase rather than the other. In the usual low-field
A-phase theB-field has a markedeffect on the vector orderingby a tendency
to alignthelocalSdirection. SinceintheA-phaseLis itself constrained to be
perpendicular to a wall (otherwise the pair would rotate into it), and there is also
adipole couplingbetween spinandorbitalmotion, thewholesystemis onein
which topological insight and imagination are required. Thus superfluid^3 Hegives
an accessible laboratory for all sorts of theoretical speculation in a whole variety
of different regions ofphysics,from cosmologyto turbulence.15 .2 Statistics in astrophysical systems
Thesimpleideas ofstatisticalphysics turn out tohave a profoundinfluence on our
understandingofsome parts ofastrophysics. We shall briefly discuss two suchareas
(out of many). In the first, according to modern (fashionable?) theory, a simple
Boltzmannfactor turns out tobeavitalfactor to tellus about thechemicalmakeup of
our universe shortlyafter thebig bang.The secondareaisatthe opposite endofthe
time-scale, in our understanding of the stability or otherwise of certain types of stellar
matter. The properties ofdense Fermi-Dirac gases are abasic part ofadiscussion of
white-dwarfstars andofneutron stars,andwe shalloutline some ofthefeatures.