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

Simple item page
dc.creatorHussein, M. S.
dc.creatorVorov, O. K.
dc.date2001-08-14
dc.date2002-03-14
dc.date.accessioned2026-07-07T02:42:24Z
dc.date.available2026-07-07T02:42:24Z
dc.descriptionUsing 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 <z_1^k z_2^l |V| z_2^m z_1^n> 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.
dc.description5 pages, minor textual revisions
dc.identifierhttps://arxiv.org/abs/cond-mat/0108216
dc.identifierhttp://arxiv.org/abs/cond-mat/0108216
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/18130
dc.subjectStatistical Mechanics
dc.subjectNuclear Theory
dc.subjectAtomic Physics
dc.subjectQuantum Physics
dc.titleOn "Do the attractive bosons condense?" by N. K. Wilkin, J. M. F. Gunn, R. A. Smith
dc.typetext

Files

Collections

arXiv