We explicitly build a generalized local-density approximation (GLDA) correlation functional based on one-dimensional uniform electron gases (UEGs). The fundamental parameters of the GLDA---a generalization of the widely known local-density approximation used in density-functional theory---are the electronic density $\ensuremath{\rho}$ and a two-electron local parameter called the hole curvature $\ensuremath{\eta}$. The UEGs considered in this study are finite versions of the conventional infinite homogeneous electron gas and consist of
n electrons on an infinitely thin wire with periodic boundary conditions. We perform a comprehensive study of these finite UEGs at high, intermediate, and low densities using perturbation theory and quantum Monte Carlo calculations. We show that the present GLDA functional yields accurate estimates of the correlation energy for both weakly and strongly correlated one-dimensional systems and can be easily generalized to higher-dimensional systems.
Analytical expressions are given for the static structure factor S(k) and the pair correlation function g(r) for uniform ideal Bose‐Einstein and Fermi‐Dirac gases for all temperatures. In the vicinity of Bose Einstein condensation (BEC) temperature, g(r) becomes long ranged and remains so in the condensed phase. In the dilute gas limit, g(r) of bosons & fermions do not coincide with Maxwell‐Boltzmann gas but exhibit bunching & anti‐bunching effect respectively. The width of these functions depends on the temperature and is scaled as √ (inverse atomic mass). Our numerical results provide the precise quantitative values of suppression/increase (antibunching and bunching) of the density fluctuations at small distances in ideal quantum gases in qualitative agreement with the experimental observation for almost non‐trapped dilute gases.
Abstract. Analytical expressions are given for the static structure factor S(k) and the pair correlation function g(r) for uniform ideal Bose-Einstein and Fermi-Dirac gases for all temperatures. In the vicinity of Bose Einstein condensation (BEC) temperature, g(r) becomes long ranged and remains so in the condensed phase. In the dilute gas limit, g(r) of bosons & fermions do not coincide with Maxwell-Boltzmann gas but exhibit bunching & anti-bunching effect respectively. The width of these functions depends on the temperature and is scaled as √ (inverse atomic mass). Our numerical results provide the precise quantitative values of suppression/increase (antibunching and bunching) of the density fluctuations at small distances in ideal quantum gases in qualitative agreement with the experimental observation for almost non-trapped dilute gases.