Book contents
- Frontmatter
- Contents
- Preface
- 1 Theory of excitations in superfluid 4He: an introduction
- 2 Dynamic response of Helium atoms to thermal neutrons
- 3 Bose broken symmetry and its implications
- 4 High-momentum scattering and the condensate fraction
- 5 Dielectric formalism for a Bose fluid
- 6 Response functions in the low-frequency, long-wavelength limit
- 7 Phonons, maxons and rotons
- 8 Sum-rule analysis of the different contributions to S(Q, ω)
- 9 Variational and parameterized approaches
- 10 Two-particle spectrum in Bose-condensed fluids
- 11 Relation between excitations in liquid and solid 4He
- 12 The new picture: some unsolved problems
- References
- Author index
- Subject index
5 - Dielectric formalism for a Bose fluid
Published online by Cambridge University Press: 23 September 2009
- Frontmatter
- Contents
- Preface
- 1 Theory of excitations in superfluid 4He: an introduction
- 2 Dynamic response of Helium atoms to thermal neutrons
- 3 Bose broken symmetry and its implications
- 4 High-momentum scattering and the condensate fraction
- 5 Dielectric formalism for a Bose fluid
- 6 Response functions in the low-frequency, long-wavelength limit
- 7 Phonons, maxons and rotons
- 8 Sum-rule analysis of the different contributions to S(Q, ω)
- 9 Variational and parameterized approaches
- 10 Two-particle spectrum in Bose-condensed fluids
- 11 Relation between excitations in liquid and solid 4He
- 12 The new picture: some unsolved problems
- References
- Author index
- Subject index
Summary
In Chapter 3, we have shown how a Bose condensate leads to the single-particle Green's function Gαβ(Q, ω) appearing as a distinct component of the the dynamic structure factor S(Q, ω). This feature is a direct consequence of (3.13) and is explicitly shown by the expression for S(Q, ω) in (3.18). In the present chapter, we review the many-body diagrammatic analysis which specifies the precise relation between Gαβ(Q, ω) and S(Q, ω) in a Bose-condensed fluid (n0 ≠ 0). The power of this “dielectric formalism” lies in showing that both functions mirror each other, as a result of the condensate-induced intermixing of single-particle and density excitations. At the same time, the formalism emphasizes the continuity of these excitations as the fluid passes through Tλ, although these excitations have very temperature-dependent weights in Gαβ(Q, ω) and S(Q, ω). While it is the poles of the single-particle Green's function which describe the elementary excitations, experimentally it is difficult to probe directly this field-fluctuation spectrum. In particular, it is only in a Bose-condensed fluid that one can obtain information about Gαβ(Q, ω) from inelastic neutron-scattering data on S(Q, ω). In the absence of a condensate, there is little relation between the density-fluctuation modes and the single-particle excitations in a Bose fluid.
After setting up the dielectric formalism in Section 5.1, the next two sections consider some model approximations at finite temperatures. These models are most appropriate to a dilute weakly interacting Bose gas (WIDBG), but we believe they also give crucial insight into various aspects of superfluid 4He.
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- Excitations in a Bose-condensed Liquid , pp. 92 - 126Publisher: Cambridge University PressPrint publication year: 1993