Dielectric formalism for a Bose fluid
Allan Griffin
In Chapter 3, we have shown how a Bose condensate leads to the single-particle Green's function G αβ ( 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 G αβ ( Q , ω) and S ( Q , ω) in a Bose-condensed fluid ( n 0 ≠ 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 T λ, although these excitations have very temperature-dependent weights in G αβ ( 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 G αβ ( 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 4 He.
Cambridge University Press eBooks•Aug 19, 1993•0 citations