Correlations of occupation numbers in the canonical ensemble and application to a Bose-Einstein condensate in a one-dimensional harmonic trap
Correlations of occupation numbers in the canonical ensemble and application to a Bose-Einstein condensate in a one-dimensional harmonic trap
We study statistical properties of $N$ noninteracting identical bosons or fermions in the canonical ensemble. We derive several general representations for the $p$-point correlation function of occupation numbers $\overline{{n}_{1}\ensuremath{\cdots}{n}_{p}}$. We demonstrate that it can be expressed as a ratio of two $p\ifmmode\times\else\texttimes\fi{}p$ determinants involving the (canonical) mean occupations $\overline{{n}_{1}}$, ..., …