Theory Of Liquid 4He

Abstract

Abstract In this section we present the dielectric formulation (DF) of the dynamics of a Bose fluid. It is called a dielectric theory because the density and single-particle response of the fluid is expressed in terms of a wavevector and frequency-dependent dielectric function ϵ (Q, ω). It is also an extension of the field theory or response function theory introduced in §§’s 8.2, 8.4, and 9.4. It represents a coherent theory of the density and single-particle response taking explicit account of the condensate.The DF has its origins in the diagrammatic studies of Bose liquids by Gavoret and Nozieres (1964) and by Hohenberg and Martin (1965). The theory may be said to have two basic motivations. Firstly, when a Bose fluid has a condensate, n 0, the density and single-particle response are coupled, via the condensate. This coupling was discussed in §8.2 where we saw that the single-particle Green function, G, appears as a term in the density dynamic susceptibility χ when there is a condensate. Similarly, the self-energy, Σ, has a term containing the dynamic susceptibility χRgiven by (8.26) and (8.58). Via this term, the density response appears in the single-particle G. The first motivation of the DF is to build this coupling of χ sind G directly in the theory. The full χ and G are expressed in terms of simpler, ‘uncoupled’ [ineq] and [ineq] and the structure of the theory will incorporate the coupling via the condensate.