On the complicate structure of a condensate for the Bose fluid in a vessel

Details On the complicate structure of a condensate for the Bose fluid in a vessel On the complicate structure of a condensate for the Bose fluid in a vessel

2012-01-10

arxiv.org/abs/1201.2185v2

Physics

Condensed Matter

Other Condensed Matter

7 pages, v2: several corrections

Scientific paper

We show that the ground state of the Bose fluid in a vessel-parallelepiped can be characterized not only by the quantum numbers p=(2\pi l_x/L_x, 2\pi l_y/L_y, 2\pi l_z/L_z) (l_x, l_y, l_z = 1, 2, 3, ...) of an expansion in the eigenfunctions e^{ipr} of a free particle, but also by the quantum numbers k_l=(\pi l_x/L_x, \pi l_y/L_y, \pi l_z/L_z) of an expansion in the eigenfunctions \sin{xk_{l_x}\sin{yk_{l_y})}\sin{zk_{l_z}} of a particle in the box. In the latter case, the one-particle condensate "is dispersed" over many lower levels with odd l_x, l_y, l_z. 53% atoms of the condensate occupy the lowest level with k=(\pi/L_x, \pi/L_y, \pi/L_z). The sum of condensates on all levels is determined by the same formula N_c/N=\rho_{\infty}, as that for the condensate on the level with p=0. The proposed k-representation supplements the traditional one (with the condensate on the level E = (hp)^{2}/2m=0) and allows one to consider the microstructure of a system from another side.

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