Excitations in Superfluid ⁴He and the Dielectric Formalism

Abstract

Despite great efforts over many years, a truly microscopic understanding of the phonon-maxon-roton spectrum in superfluid ⁴He has continued to be elusive. High resolution neutron scattering studies^1,2,3 of the lineshape exhibited by $S(\vec{Q},\omega )$ have given vivid evidence of the completely different behaviour of the low Q phonon spectrum and the high Q maxon-roton spectrum as the temperature increases towards T _λ. Recently, Glyde and the author have realized that recent experimental results gave the needed clues which were missing before. We have proposed a unified theory⁴ of the excitations in superfluid ⁴He which is firmly anchored in the existence of a Bose broken symmetry (see Sokol, these proceedings). We believe that a suitably parameterized version of this microscopic formulation will provide a natural starting point for detailed comparisons with the excitations observed in high resolution neutron scattering data. For further discussion of its experimental implications, we refer to the papers by Glyde and Svensson in these proceedings. The main goals of this article are to discuss the basic elements of the new picture, to review its historical development and relation to earlier ideas, and finally, to sketch how it might be brought into contact with the very successful phenomenological approach based on variational many body wavefunctions.