Progress of Theoretical Physics

Momentum Distribution of an Interacting Many-Boson System at High Density

T. Nishiyama

Published Jul 1, 1976• 0 citations

Abstract

The momentum distribution function np is obtained for an interacting many-boson system at high density using the Rayleigh-Schrödinger perturbation theory in the scheme of the density and phase operator approach (DPO). The expression obtained has a correct form in the low momentum limit in accord with the condition first given by Gavoret and Nozières. The origin of an unphysical result found by Grest that np becomes negative for low wave numbers will be elucidated. Using the expression for np the ground-state energy is re-obtained. The result agrees completely with that given by Brueckner and Lee.

DOI: 10.1143/ptp.56.16

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Progress of Theoretical Physics

Momentum Distribution of an Interacting Many-Boson System at High Density

T. Nishiyama

Published Jul 1, 1976• 0 citations

Publisher

Abstract

DOI: 10.1143/ptp.56.16

Related papers

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Physical review. B, Solid stateJun 1, 19753 citations

g(r)

is the radial distribution function and

{N}_{0}

is the mean occupation number of the zero-momentum state. In the uniform limit the variation-perturbation approach based on (a) the method of correlated basis functions and (b) the series expansion in powers of $\ensuremath{\alpha}$ is found to be equivalent to the field-theoretic treatment given by Brueckner (for the charged-boson gas) in the weak coupling limit. In particular, it is shown that the variation-perturbation energy obtained for the uniform limit in the momentum representation is identical through second order to the ground-state energy evaluated for $\ensuremath{\beta}\ensuremath{\ll}1$ by summing one- and two-ring diagrams in the Bogoliubov occupation-number representation. The charged-boson gas and the one-dimensional boson system with a $\ensuremath{\delta}$-function interaction are considered to examine some of the interesting features of the uniform-limit procedure.

E(\mathrm{k})

of a phonon of momentum k, which is found as the pole of a one-particle Green's function, approaches zero for zero momentum, which means that the phonon spectrum does not exhibit an energy gap.The Green's function method is applied to the calculation of the properties of a low-density boson gas. The next order term beyond that calculated by Lee and Yang, and Beliaev for the ground-state energy is obtained and the general form of the series expansion is found to be $(\frac{{E}_{0}}{\ensuremath{\Omega}})=\frac{1}{2}{n}^{2}{f}_{0}[1+a{(n{{f}_{0}}^{3})}^{\frac{1}{2}}+b(n{{f}_{0}}^{3})\mathrm{ln}n{{f}_{0}}^{3}+c(n{{f}_{0}}^{3})+d{(n{{f}_{0}}^{3})}^{\frac{3}{2}}\mathrm{ln}(n{{f}_{0}}^{3})+\ensuremath{\cdots}],$ where

n

is the density and

{f}_{0}

is the scattering length for the assumed two-body interaction between the bosons. The coefficients

a

and

b

are independent of the shape of the interaction, and are the only terms thus far calculated. The coefficient

b

is in agreement with the hard-sphere gas calculations of Wu and of Sawada.A discussion is given of the intermediate-density calculation of Brueckner and Sawada, and certain possible improvements in the method of summing a selected set of higher-order terms are proposed.