Title
Boson and fermion many-body assemblies: fingerprints of excitations in the ground-state wave functions, with examples of superfluid <tex>$^{4}He$</tex> and the homogeneous correlated electron liquid Boson and fermion many-body assemblies: fingerprints of excitations in the ground-state wave functions, with examples of superfluid <tex>$^{4}He$</tex> and the homogeneous correlated electron liquid
Author
Faculty/Department
Faculty of Sciences. Physics
Publication type
article
Publication
London ,
Subject
Physics
Source (journal)
Physics and chemistry of liquids. - London
Volume/pages
46(2008) :5 , p. 465-480
ISSN
0031-9104
ISI
000260382800001
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
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.
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