Boson and fermion many-body assemblies: fingerprints of excitations in the ground-state wave functions, with examples of superfluid ⁴He and the homogeneous correlated electron liquid

Abstract

After a brief summary of some basic properties of ideal gases of bosons and of fermions, two many-body Hamiltonians are cited for which ground-state wave functions allow the generation of excited states. Because of the complexity of ground-state many-body wave functions, we then consider properties of reduced density matrices, and in particular, the diagonal element of the second-order density matrix. For both the homogeneous correlated electron liquid and for an assembly of charged bosons, the ground-state pair correlation function g(r) has fingerprints of the zero-point energy of the plasmon modes. These affect crucially the static structure factor, S(k), in the long wavelength limit. This is best understood by means of the Ornstein–Zernike direct correlation function c(r), which plays an important role throughout this article. Turning from such charged liquids, both boson and fermion, to superfluid ⁴He, the elevated temperature (T) structure factor S(k, T) is related, albeit approximately, to its zero-temperature counterpart, via the velocity of sound, reflecting the collective phonon excitations and the superfluid density. Finally, some future directions are pointed.

Keywords:

• superfluid ⁴He
• homogeneous electron liquid
• charged bose fluid

Acknowledgements

This article was brought to fruition during a stay at the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy. The author is greatly indebted to Professors V.E. Kravtsov and E. Tosatti for the very stimulating environment and for exceptionally generous hospitality. Extensive discussions on the general area embraced by this article with Professors C. Amovilli, J. Mayers, M.P. Tosi and W.H. Young are gratefully acknowledged.