On "Do the attractive bosons condense?" by N. K. Wilkin, J. M. F. Gunn, R. A. Smith

Details On "Do the attractive bosons condense?" by N. K. Wilkin, J. M. F. Gunn, R. A. Smith On "Do the attractive bosons condense?" by N. K. Wilkin, J. M. F. Gunn, R. A. Smith

2001-08-14

arxiv.org/abs/cond-mat/0108216v3

Physics

Condensed Matter

Statistical Mechanics

5 pages, minor textual revisions

Scientific paper

Using Perron-Frobenius theorem, we prove that the results by Wilkin, Gunn and Smith [1] for the ground states of N Bose atoms rotating at the angular momentum L in a harmonic atomic trap with frequency omega interacting via attractive delta^2(r) forces, are valid for a broad class of predominantly attractive interactions V(r), not necessarily attractive for any r. The sufficient condition for the interaction is that all the two-body matrix elements allowed by the conservation of angular momentum k+l = m+n, are negative. This class includes, in particular, the Gaussian attraction of arbitrary radius, -1/r - Coulomb and log(r)-Coulomb forces, as well as all the short-range R << omega^{-1/2} interactions satisfying inequality int d^2r V(r) < 0. There is no condensation at L>> 1, and the angular momentum is concentrated in the collective ``center-of-mass'' mode.

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