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Journal de Physique IV (Proceedings)

The ground-state energy of the quasi-one-dimensional charged Bose condensate

L. Calmels, Alfred Gold

Published Mar 1, 2000• 0 citations
Publisher

Abstract

In a recent paper we studied the ground-state energy of a quasi-one dimensional charged Bose condensate confined by a two-dimensional oscillator potential [l]. Many-body effects beyond the RPA have been taken into account by the local-field correction. In the present paper we study a quasi-one dimensional charged Bose condensate with a cylindrical confinement model (hard walls) and compare with the results of an electron gas. The following quantities are calculated : interaction energy, pair-correlation function, local-field correction, dielectric function, collective modes.

DOI
10.1051/jp4:2000565

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In a recent paper we studied the ground-state energy of a quasi-one dimensional charged Bose condensate confined by a two-dimensional oscillator potential [l]. Many-body effects beyond the RPA have been taken into account by the local-field correction. In the present paper we study a quasi-one dimensional charged Bose condensate with a cylindrical confinement model (hard walls) and compare with the results of an electron gas. The following quantities are calculated : interaction energy, pair-correlation function, local-field correction, dielectric function, collective modes.
We describe correlation effects in the charged quasi-one-dimensional Bose condensate with parabolic confinement. Many-body effects are calculated with the sum-rule version of the Singwi, Tosi, Land, and Sj\"olander theory. We give numerical and analytical results for the local-field correction, the pair-distribution function, the correlation energy, and the compressibility of the Bose condensate. The results are given as a function of the Wigner-Seitz parameter rs{r}_{s}rs​ and the wire-width parameter b.b.b. The exact long-wavelength behavior of the plasmon dispersion is investigated using the compressibility sum rule.
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 the quasi-two-dimensional Bose liquid in a periodic one-body potential is examined. The energy shift and density variation due to the periodic potential are calculated with a procedure which combines the paired-phonon analysis and canonical transformations. The results of this calculation are compared to the recent calculation of these effects which employed a correlated wave function and a cumulant expansion. The results are the same to lowest order. The advantages and disadvantages of each technique are explored.
We consider the integrable one-dimensional δ-function interacting Bose gas in a hard wall box which is exactly solved via the coordinate Bethe ansatz. The ground-state energy, including the surface energy, is derived from the Lieb– Liniger-type integral equations. The leading and correction terms are obtained in the weak and strong coupling regimes from both the discrete Bethe equations and the integral equations. This allows the investigation of both finite-size and boundary effects in the integrable model. We also study the Luttinger liquid behaviour by calculating Luttinger parameters and correlations. The hard wall boundary conditions are seen to have a strong effect on the ground-state energy and phase correlations in the weak coupling regime. Enhancement of the local two-body correlations is shown by application of the Hellmann–Feynman theorem. PACS numbers: 05.30.−d, 67.40.Db, 05.30.Jp (Some figures in this article are in colour only in the electronic version) 1.
We consider the integrable one-dimensional δ-function interacting Bose gas in a hard wall box which is exactly solved via the coordinate Bethe ansatz. The ground-state energy, including the surface energy, is derived from the Lieb–Liniger-type integral equations. The leading and correction terms are obtained in the weak and strong coupling regimes from both the discrete Bethe equations and the integral equations. This allows the investigation of both finite-size and boundary effects in the integrable model. We also study the Luttinger liquid behaviour by calculating Luttinger parameters and correlations. The hard wall boundary conditions are seen to have a strong effect on the ground-state energy and phase correlations in the weak coupling regime. Enhancement of the local two-body correlations is shown by application of the Hellmann–Feynman theorem.
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.