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Physical review. B, Solid state

Dielectric response of the charged Bose gas in the random-phase approximation

S. R. Hore, Norman E. Frankel

Published Oct 1, 1975• 58 citations
Publisher

Abstract

A closed form for the dielectric function of a charged Bose gas is found in the random-phase approximation. This dielectric constant is used to explore the quasiparticle energy spectrum (i.e., the allowed modes of oscillation of the gas), the damping of these quasiparticles, and the long-ranged form of the electrostatic potential around a test charge in the gas. We do this around the three temperature regions of interest; namely, $T=0$, $T=\ensuremath{\infty}$, and $T={T}_{c}$, where ${T}_{c}$ is the transition temperature of the gas.

DOI
10.1103/physrevb.12.2619

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Physical Review•Jul 5, 1967•70 citations
A closed form for the dielectric function of a charged Bose gas is found in the random-phase approximation. This dielectric constant is used to explore the quasiparticle energy spectrum (i.e., the allowed modes of oscillation of the gas), the damping of these quasiparticles, and the long-ranged form of the electrostatic potential around a test charge in the gas. We do this around the three temperature regions of interest; namely, T=0T=0T=0, T=\ensuremath∞T=\ensuremath{\infty}T=\ensuremath∞, and T=TcT={T}_{c}T=Tc​, where Tc{T}_{c}Tc​ is the transition temperature of the gas.
The dielectric response of the two-dimensional charged Bose gas is investigated in the random-phase approximation. Using this temperature-dependent dielectric function we find the energy spectrum and the damping for the quasiparticles. The electrostatic potential around a test charge at T=0T=0T=0 is displayed. We also study the thermodynamic functions of the gas at very low temperatures and high densities.
The dielectric function of a charged Bose gas is determined from the response to an imposed static sinusoidal electric field. Variational and diffusion quantum Monte Carlo simulations are used to calculate the ground-state properties of the system with trial wave functions containing a parameter dependent on the amplitude and wavelength of the perturbation. The induced charge is most efficiently extracted from the difference in ground-state energies at different magnitudes of the external field, rather than directly from the expectation value of the density fluctuation operator. Results are compared to the random-phase approximation for the weakly coupled fluid and to classical lattice values at low densities where the system forms a Wigner crystal. The dielectric function is also calculated at intermediate fluid densities and the transition from positive to negative response is found to occur in the metallic regime.
The self-consistent random-phase approximation is used to derive an integral equation for the quasiparticle energy of a charged Bose gas near a critical point. An approximate analytical solution, valid at long wavelengths, is used to compute the critical exponents which are those of an ideal Bose gas with the single-particle spectrum $\ensuremath{\epsilon}(p)=A{p}^{2\ensuremath{-}\ensuremath{\eta}},\ensuremath{\eta}\ensuremath{\simeq}0.2$. The accuracy of the analytical solution is checked by an exact numerical solution which is also used in a calculation of the transition curve. A necessary condition for the correctness of the theory is found to be $\frac{(T\ensuremath{-}{T}_{c})}{{T}_{c}}\ensuremath{\gg}0.01$.
The main focus of this work is on the predictions made by the dielectric formalism in regard to the relationship between single-particle and collective excitation spectra in a gas of pointlike charged bosons at finite temperature TTT below the critical region of Bose-Einstein condensation. Illustrative numerical results at weak coupling (rs=1)({r}_{s}=1)(rs​=1) are presented within the random phase approximation. We show that within this approach the single-particle spectrum forms a continuum extending from the transverse to the longitudinal plasma mode frequency and leading to a double-peak structure as TTT increases, whereas the density fluctuation spectrum consists of a single broad peak. We also discuss the momentum distribution and the superfluidity of the gas.
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.