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Physical Review B

Dynamic many-body theory: Pair fluctuations in bulk H4e

C. E. Campbell, E. Krotscheck

Published Nov 2, 2009• 21 citations
Publisher

Abstract

Dynamical excitations in bulk liquid $^{4}\text{H}\text{e}$ are investigated by using a manifestly microscopic theory of excitations that includes multiple-phonon scattering. The wave function of the dynamic system is represented in terms of one- and two-body excitation amplitudes. Equations of motion for the linear response of boson liquids to a scalar external field are then derived from a stationarity principle. For a consistent treatment of long- and short-wavelength properties of the excitation amplitudes we derive and solve three sets of generic ``hypernetted chain'' equations determining the basic ingredients of the theory. From those ingredients, we calculate a dynamic structure function for $^{4}\text{H}\text{e}$ at saturation density. It is shown that the complete solution of the hypernetted chain equations leads, partly by the cancellation of errors, to an insignificantly improved theoretical prediction for the dynamic structure function compared with approximations introduced by Jackson, Feenberg, and Campbell. The implications of this result and the need for including higher-order multiparticle fluctuations are discussed.

DOI
10.1103/physrevb.80.174501

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Time-dependent multiparticle correlation functions and response functions are formulated with the functional derivatives in the grand-canonical ensemble. Equations for the single-particle Green's functions are the Dyson equations describing scattering of the single particles by density-fluctuation excitations. Equations for the density-fluctuation excitations are truncated with a dynamic version of the convolution approximation to triple correlations. A closed set of equations for the Green's functions and excitations are thereby obtained, which constitutes a dynamic hypernetted-chain scheme for the degenerate electron liquids. The formalism is extended also to the description of the spin-dependent response and correlations.
We present further progress in a systematic approach to the microscopic understanding of the dynamics of strongly interacting quantum fluids. Employing the concept of dynamic multiparticle fluctuations, we derive equations of motion for fluctuating nnn-body densities. We apply the theory to calculate the dynamic structure function of liquid 4He^{4}\mathrm{He}4He as a function of density and find, without any phenomenological input, overall excellent agreement with both experiments and, as far as available, simulation data.
Ground-state properties of a two-dimensional fluid of bosons with repulsive dipole-dipole interactions are studied by means of the Euler-Lagrange hypernetted-chain approximation. We present a self-consistent semianalytical theory of the pair distribution function g(r)g(r)g(r) and ground-state energy of this system. Our approach is based on the solution of a zero-energy scattering Schr\"odinger equation for the ``pair amplitude'' g(r)\sqrt{g(r)}g(r)​ with an effective potential from Jastrow-Feenberg correlations. We find excellent agreement with quantum Monte Carlo results over a wide range of coupling strength, nearly up to the critical coupling for the liquid-to-crystal quantum phase transition. We also calculate the one-body density matrix and related quantities, such as the momentum distribution function and the condensate fraction.
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