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Physical review. B, Solid state

Zero-temperature dielectric response of the charged Bose gas in a uniform magnetic field

S. R. Hore, Norman E. Frankel

Published Sep 1, 1976• 24 citations
Publisher

Abstract

A closed-form expression for the dielectric function of a zero-temperature charged Bose gas in a uniform magnetic field is obtained in the random-phase approximation. This dielectric function is used to explore the dispersion relation for the frequencies of longitudinal oscillation of the gas as well as the form of the electrostatic potential about a test charge in the gas.

DOI
10.1103/physrevb.14.1952

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Physical Review A•Mar 1, 1972•3 citations
A closed-form expression for the dielectric function of a zero-temperature charged Bose gas in a uniform magnetic field is obtained in the random-phase approximation. This dielectric function is used to explore the dispersion relation for the frequencies of longitudinal oscillation of the gas as well as the form of the electrostatic potential about a test charge in 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.
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, $T=\ensuremath{\infty}$, and T=TcT={T}_{c}T=Tc​, where Tc{T}_{c}Tc​ is the transition temperature of the gas.
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.
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.
By using the Bohm-Pines and Bogoliubov formalisms as well as the random-phase approximation, the investigation of the charged Bose gas is extended into the intermediate densities for which ${r}_{s}\ensuremath{\lesssim}O(1)$. The ground state energy is essentially correlation energy, and is therefore negative as expected. The expression for the plasmon spectrum does possess an energy gap; the single-particle excitation spectrum does not. The specific-heat function is examined to first order in the temperature and is shown to approach zero from above as the temperature does the same. Finally, the expression for the pressure is shown to persist in remaining negative for all ${r}_{s}\ensuremath{\lesssim}O(1)$ at zero temperature.