2001/08/14 by M. S. Hussein, Hussein, M. S., O. K. Vorov +1
Physics and Astronomy · #Atomic Physics (physics.atom-ph) #FOS: Physical sciences #Nuclear Theory (nucl-th) #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #nucl-th #physics.atom-ph #quant-ph
paper · pdf · doi:10.48550/arxiv.cond-mat/0108216
5 pages, minor textual revisions
arxiv created 2002/03/14 · arxiv updated 2009/11/30
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 delta2(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 <z1k z2l |V| z2m z1n> 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 d2r V(r) < 0. There is no condensation at L>> 1, and the angular momentum is concentrated in the collective ``center-of-mass'' mode.