Phys. Rev. A 62, 061602(R) (2000) [4 pages]Exact eigenstates for repulsive bosons in two dimensions
We consider a model of N two-dimensional bosons in a harmonic potential with weak repulsive δ-function interactions. We show analytically that, for angular momentum L<~N, the elementary symmetric polynomials of particle coordinates measured from the center of mass are exact eigenstates with energy N(N-L/2-1). Extensive numerical analysis confirms that these are actually the ground states, but we are currently unable to prove this analytically. The special case L=N can be thought of as the generalization of the usual superfluid one-vortex state to Bose-Einstein condensates in a trap. © 2000 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.62.061602
DOI:
10.1103/PhysRevA.62.061602
PACS:
03.75.Fi, 05.30.Jp, 67.40.Db, 67.40.Vs
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