Fluctuations and lambda phase transition in liquid helium

R. A. Ferrell, N. Menyhàrd, H. Schmidt, F. Schwabl, P. Szépfalusy

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Abstract

A general dynamical scaling theory of phase transitions is established by exploiting the absence of a characteristic length in an extended system at its phase transition. This similarity property imposes strong constraints on the frequency and wave-number dependence of the fluctuation spectrum and leads to unambiguous predictions concerning the critical properties. The theory is worked out in detail for the lambda transition of liquid Helium, as a prototype. The fluctuations resulting from density waves at low temperature and from both first and second sound at higher temperatures, are closely examined. The connection between the divergent fluctuations in the second sound modes (as the temperature T approaches the lambda temperature Tλ) and the critical variation of the damping coefficients is established. The critical temperature dependences of the thermal conductivity of He I and the damping of first and second sound in He II are predicted to be essentially (T - Tλ) -1 3, (Tλ - T)-1, and (Tλ - T) -1 3. (There occur also logarithmic factors.) Recent experimental measurements of the first and second of these give quantitative verification of the theory. In addition to the temperature dependence, the dynamical scaling theory does not employ any adjustable parameter and consequently also predicts the absolute magnitude of these quatities. Although this is a less conclusive check on the theory, the agreement is also satisfactory.

Original languageEnglish
Pages (from-to)565-613
Number of pages49
JournalAnnals of Physics
Volume47
Issue number3
Publication statusPublished - May 1968

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liquid helium
acoustics
damping
scaling
temperature dependence
critical temperature
thermal conductivity
prototypes
temperature
coefficients
predictions

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Ferrell, R. A., Menyhàrd, N., Schmidt, H., Schwabl, F., & Szépfalusy, P. (1968). Fluctuations and lambda phase transition in liquid helium. Annals of Physics, 47(3), 565-613.

Fluctuations and lambda phase transition in liquid helium. / Ferrell, R. A.; Menyhàrd, N.; Schmidt, H.; Schwabl, F.; Szépfalusy, P.

In: Annals of Physics, Vol. 47, No. 3, 05.1968, p. 565-613.

Research output: Contribution to journalArticle

Ferrell, RA, Menyhàrd, N, Schmidt, H, Schwabl, F & Szépfalusy, P 1968, 'Fluctuations and lambda phase transition in liquid helium', Annals of Physics, vol. 47, no. 3, pp. 565-613.
Ferrell RA, Menyhàrd N, Schmidt H, Schwabl F, Szépfalusy P. Fluctuations and lambda phase transition in liquid helium. Annals of Physics. 1968 May;47(3):565-613.
Ferrell, R. A. ; Menyhàrd, N. ; Schmidt, H. ; Schwabl, F. ; Szépfalusy, P. / Fluctuations and lambda phase transition in liquid helium. In: Annals of Physics. 1968 ; Vol. 47, No. 3. pp. 565-613.
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