Superfluid density in He II near the lambda transition: First principles theory

A first principles theory of the lambda transition in liquid He-4 was introduced in a recent paper [H. W. Jackson, J. Low Temp. Phys. 155, 1 (2009)]. In that theory critical fluctuations consisting of isothermal fourth sound waves are treated with quantum statistical mechanics methods in deriving formulas for constant volume conditions for specific heat, correlation length, equal time pair correlation function, and isothermal compressibility. To leading order terms in (T-lambda - T) the theory yields exact results alpha' =0 and nu'=2/3 for critical exponents at constant volume. A follow-up study in the present paper demonstrates by a least squares fit that a logarithmic function accurately describes the specific heat at svp when (T-lambda- T) is between 10(-9) K and 10(-5) K. This logarithmic divergent behavior conflicts with previous analyses of experimental data and predictions of renormalization group theory that constant pressure specific heat is finite at T-lambda, but Is thermodynamically consistent with logarithmic asymptotic behavior of specific heat at constant volume predicted in the new theory. The first principles theory is extended in this paper to derive formulas for superfluid density and for a relation between superfluid density and correlation length in He If near T-lambda. Numerical results based on these formulas are in good agreement with experimental data produced by second sound measurements. (C) 2014 Elsevier B.V. All rights reserved.