Physics – Condensed Matter – Quantum Gases
Scientific paper
2012-01-29
Physics
Condensed Matter
Quantum Gases
7 pages, 10 figures
Scientific paper
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.
Li Xue Chao
Wang An Min
Wang Zhao Liang
Yang Yang
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