12 - The new picture: some unsolved problems

Summary

In this book, we have developed the theory of the excitation spectrum of superfluid ⁴He in which the Bose condensate plays the central role. In Chapter 5, we showed how a Bose broken symmetry inevitably leads to a mixing of the single-particle and density fluctuations. Combining the general results of the dielectric formalism with recent high-resolution neutron-scattering data over a wide range of wavevectors, energies and temperatures, we were led in Chapter 7 to a new interpretation of the well known phonon–maxon–roton dispersion curve. In Section 12.1, we briefly recapitulate this new scenario and discuss how it developed from preceding theoretical work. We also review earlier studies which had independently suggested that rotons were in fact atomic-like single-particle excitations, quite different from the long-wavelength phonons. In addition, we address the question of what Feynman's work says about the nature of rotons.

The most important topic which has not been covered in this book is superfluid ³He–⁴He mixtures. The appropriate dielectric formulation has been developed by Talbot and Griffin (1984c), as we briefly summarize in Section 12.2. Much work remains to be done in using these formal results in a detailed analysis of experimental S(Q, ω) data, even at the level of Section 7.2 in the case of pure ⁴He.

Finally, in Section 12.3, we list some specific topics where further theoretical and experimental work would be useful. This list, which brings together suggestions scattered throughout the book, also acts as a convenient summary of our major themes.