Ground state of a homogeneous Bose gas of hard spheres

The ground state of a homogeneous Bose gas of hard spheres is treated in self-consistent mean-field theory. It is shown that this approach provides an accurate description of the ground state of a Bose-Einstein condensed gas for arbitrarily strong interactions. The results are in good agreement with Monte Carlo numerical calculations. Since all other mean-field approximations are valid only for very small gas parameters, the present self-consistent theory is a unique mean-field approach allowing for an accurate description of Bose systems at arbitrary values of the gas parameter.

Figure 1

Condensate fraction $n_0$ (solid line) as a function of the gas parameter $\gamma$, compared with the Monte Carlo results by Rossi and Salasnich [13], shown by dots, and with the Bogoliubov approximation $n_B$ (dashed line). The latter is not applicable above $\gamma =0.1$.

Figure 2

Fraction of uncondensed atoms $n_1$ (solid line) and anomalous average $\sigma$ (dash-dotted line) as functions of the gas parameter $\gamma$. The anomalous average is everywhere larger than the $n_1$.

Figure 3

Sound velocity $s$ (solid line) in dimensionless units, compared with the Bogoliubov sound velocity $s_B$ (dashed line), as functions of $\gamma$. The Bogoliubov approximation essentially deviates from $s$ above $\gamma =0.1$.

Figure 4

Dimensionless ground-state energy $E_0$ (solid line) as a function of the gas parameter $\gamma$, compared with the Monte Carlo results by Rossi and Salasnich [13], shown by dots, and with the Lee-Huang-Yang expression $E_{\text{LHY}}$ (dashed line). The latter deviates from the numerical data after $\gamma =0.4$.