ABSTRACT
We conclude our study of superfluidity in Bose liquids with a brief summary of the strengths, and of the inadequacies, of the theory. The cornerstone of our fundamental understanding of superfluidity has been the recognition of the central importance of the condensate, a single quantum state which is macroscopically occupied. For the Bose liquid one has a particle condensate, characterized by a non-vanishing expectation value of ψ(r). The existence of the condensate explains all major aspects of superfluid behavior; in particular, we now possess:
A clear understanding of the static and the long wavelength dynamic properties of an equilibrium Bose liquid, including a microscopic basis for the two-fluid model.
A precise microscopic theory at T = 0 for a specific model, the dilute Bose gas.
Variational calculations of the excitation spectrum of liquid He II (and of the ground state properties as well), which are in good quantitative agreement with experiment.
A satisfactory phenomenological treatment of the interactions between elementary excitations which give rise to various irreversible phenomena.
A qualitative understanding of the role which is played by quantized vortices in both equilibrium and non-equilibrium phenomena.
