Fluctuations and lambda phase transition in liquid helium

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 T λ ) 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 − T λ ) −1 3 , ( T λ − T ) −1 , and (T λ − 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.