FOUNDATIONS OF A COMPREHENSIVE THEORY OF LIQUID-HE-4

A theory of liquid He4 is formulated that incorporates the principal elements of approaches found most successful in the past. It is grounded in quantum-mechanical correlated-basis-function formalism, which produces an elementary-excitation model for the flowing liquid. Standard statistical-mechanical techniques are used to derive explicit formulas for thermodynamic and hydrodynamic properties that are relevant to the macroscopic two-fluid equations. An important feature of this work is that it produces an explicit formula for the Lagrangian used by Zilsel to derive the two-fluid equations from a variational principle. The general formulas developed here take into account effects of interactions and constraints involving elementary excitations. It is demonstrated that temperature-dependent energy levels occur in ordinary statistical-mechanical formulas as a consequence of interactions. The fact that energy widths of elementary excitations do not enter the formulas is discussed. The formulas are applied to some simple models, and they are used there in a detailed study of the specific heat. Temperature and flow dependence of thermodynamic variables are exhibited in graphical form. It is observed that the Helmholtz potential has a peculiar behavior, and the possibility that this is connected with the changing flow properties at Tλ is studied within the context of a stability analysis involving general thermodynamic criteria. That same potential suggests that a state of flow may be thermodynamically preferred over the rest state for a range of temperatures reaching somewhat below Tλ. This is one factor that motivates a calculation of properties of quantized vortices in the liquid in the final section of the paper. © 1979 The American Physical Society.