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TURKISH JOURNAL OF PHYSICS

A note on the generalization of Bijl-Feynman spectrum to multi-component systems with an application to double-layer charged Bose gas

B. Tanatar

Published Jan 1, 1996• 0 citations
Publisher

Abstract

We consider the generalization of Bijl-Feynman excitation energy formula to multi-component Bose fluids. Identification of these excitation energies with those obtained from the poles of the density-density response function simplifies the calculation of static structure factors Sij(q) . This in turn helps simplify the self-consistent calculations that go beyond the usual random-phase approximation. We illustrate our approach by evaluating the structure factors and local-field corrections in a double-layer charged Bose gas. © Tübi̇tak.

DOI
10.55730/1300-0101.2633

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We consider the generalization of Bijl-Feynman excitation energy formula to multi-component Bose fluids. Identification of these excitation energies with those obtained from the poles of the density-density response function simplifies the calculation of static structure factors Sij(q) . This in turn helps simplify the self-consistent calculations that go beyond the usual random-phase approximation. We illustrate our approach by evaluating the structure factors and local-field corrections in a double-layer charged Bose gas. © Tübi̇tak.
The ground state of a charged Bose gas is studied throughout a large range of densities in a self-consistent-field approximation formalism which includes the short-range correlations between bosons through a local-field correction. Numerical self-consistent calculations have been carried out in order to determine the static structure factor $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$. Hence, from $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ we have obtained the pair-correlation functions, the ground-state energy which essentially is the correlation energy, the pressure of the gas, and, from Feynman's relation, the energy spectrum of elementary excitations. The response of the system to a static impurity charge has also been investigated. In the high-density limit our calculations show the same results as those given by Bogoliubov's perturbation theory. In the intermediate-density region, corresponding to the strongly coupled system, our results are in very good agreement with recent calculations based on the hypernetted-chain integral equation as well as Monte Carlo computations.
This is the first of two papers in which the high-density charged Bose gas at zero temperature is treated by two independent and self-contained methods. In this paper, we are concerned with the excitation spectrum of the system. An analysis of the formal and physical aspects of the theory is followed by a simple numerical calculation. We apply the usual field-theoretic formulation for a Bose system. The Green's functions and other response functions, or propagators, are analyzed, emphasizing the role of the dielectric constant. The general features of the excitation spectrum are described. To apply and to further illustrate the formalism, the low-lying levels are numerically determined to the order of rs34{{r}_{s}}^{\frac{3}{4}}rs​43​ in units of ${\ensuremath{\omega}}_{\mathrm{pl}}$ (the next order beyond the Bogoliubov approximation). rs{r}_{s}rs​ is the ratio of the average interparticle distance to the Bohr radius and ${\ensuremath{\omega}}_{\mathrm{pl}}$ is the plasma frequency.
We study many-body effects of a charged-boson system in terms of a dynamically self-consistent method. We calculate static structure factors, elementary excitation energies, pair correlation functions, and ground-state energies for various densities through the iterative calculation using two independent relations between the structure factor and the local-field correction, and compare with a similar method using the local-field correction of Singwi et al. We claim that our ground-state energies may be considered as lower bounds.
The ground state of a double-layer charged Bose system is investigated beyond the random-phase approximation by including the many-body correlation effects. The correlations within the layer are accounted for within the self-consistent theory of Singwi, Tosi, Land, and Sj\"olander, while we have neglected the effect of interlayer correlations. The static susceptibility, the elementary excitation spectrum, and the static screened potentials are calculated and their dependence on the boson number density and the layer spacing is examined. Results are compared with the recent work of Tanatar and Das where correlations are not included. It is found that the inclusion of correlation effects combined with the interlayer interactions can significantly alter the nature of the ground state and, in particular, can favor an inhomogeneous charge-density-wave ground state. A comparison is also made in terms of screened potentials with the double-layer electron system that enables one to have a deeper insight into the role played by the exchange and Coulomb correlations separately.
The excitation spectrum of a charged Bose gas in the high-density limit is calculated to two orders in the expansion parameter rs34{r}_{s}^{\frac{3}{4}}rs43​​ by the method of correlated basis functions (CBF). To O(rs34)O({r}_{s}^{\frac{3}{4}})O(rs43​​), the result differs from that obtained variationally, but agrees with that obtained by Ma and Woo via diagrammatic perturbation theory. The choice of the basis functions is, however, not unique. By choosing an alternate set of CBF which employs the ground-state eigenfunction as a correlating factor, we find it possible to extract from the excitation spectrum an expression for the liquid-structure function, also to two orders in rs34{r}_{s}^{\frac{3}{4}}rs43​​, which represents a new result. This new facet of CBF helps to demonstrate the flexibility of the method and the ease with which it can be applied to calculating properties of many-particle systems, model as well as realistic.
The static-linear-response function $\ensuremath{\chi}(k)$ is derived for the quantum Bose fluid with the use of the hypernetted-chain approximation in the Jastrow theory. The pair-correlation function of the uniform system required as an input function is optimized within the same theory. The compressibility sum rule as well as the sequential and screening conditions are exactly fulfilled by construction. It is shown analytically that in the small-wavelength limit the leading correction in ${\ensuremath{\chi}}^{\ensuremath{-}1}(k)$ to the freeparticle kinetic energy is a constant 23TJFN\frac{2}{3}\frac{{T}_{\mathrm{JF}}}{N}32​NTJF​​, where TJF{T}_{\mathrm{JF}}TJF​ is the Jackson-Feenberg kinetic energy. We have also developed a reliable numerical method which is used in the calculation of the linear-response function of the charged-boson gas at metallic densities.