Finite one dimensional impenetrable Bose systems: Occupation numbers

Details Finite one dimensional impenetrable Bose systems: Occupation numbers Finite one dimensional impenetrable Bose systems: Occupation numbers

2002-11-07

arxiv.org/abs/cond-mat/0211126v1

Physics

Condensed Matter

22 pages, 8 figures (.eps), uses REVTeX4

Scientific paper

10.1103/PhysRevA.67.043607

Bosons in the form of ultra cold alkali atoms can be confined to a one dimensional (1d) domain by the use of harmonic traps. This motivates the study of the ground state occupations $\lambda_i$ of effective single particle states $\phi_i$, in the theoretical 1d impenetrable Bose gas. Both the system on a circle and the harmonically trapped system are considered. The $\lambda_i$ and $\phi_i$ are the eigenvalues and eigenfunctions respectively of the one body density matrix. We present a detailed numerical and analytic study of this problem. Our main results are the explicit scaled forms of the density matrices, from which it is deduced that for fixed $i$ the occupations $\lambda_i$ are asymptotically proportional to $\sqrt{N}$ in both the circular and harmonically trapped cases.

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