## Relations Among Some Ground-state properties of a Bose Gas in Periodic Potentials    [PDF]

Zhao Liang Wang, An Min Wang, Xue Chao Li, Yang Yang
The relations among the occupation number of the lowest natural orbital,
momentum distributions and off-diagonal elements of the reduced single-particle
density matrix (RSPDM) are studied while a Bose gas in periodic potentials is
in the ground state. For large particle number systems, RSPDM and its lowest
natural orbital of $N$-body system are the same as that of $(N+1)$-body system
in overlapped areas in both commensurate and incommensurate cases. For large
$N$ in commensurate case, the occupation number of the lowest natural orbital
and momentum distributions (MD) are invariant with $N$ that results from the
exponential attenuation with $N$ of the off-diagonal elements. While in
contrast, in incommensurate case, the off-diagonal elements are inversely
proportional to $\sqrt{N}$, which result in the different behavior of the
occupation number of the lowest natural orbital and MD. There are no
Bose-Einstein condensation (BEC) for periodic trapped TG gas in both
commensurate and incommensurate cases.
View original: http://arxiv.org/abs/1201.6019