Exact Eigenstates for Repulsive Bosons in Two Dimensions

England); N K Wilkin (University of Birmingham; R A Smith

Exact Eigenstates for Repulsive Bosons in Two Dimensions

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arxiv cond-mat/0005230 v1 pith:MVG74SZF submitted 2000-05-14 cond-mat

Exact Eigenstates for Repulsive Bosons in Two Dimensions

R A Smith , N K Wilkin (University of Birmingham , England) This is my paper

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We consider a model of $N$ two-dimensional bosons in a harmonic potential with weak repulsive delta-function interactions. We show analytically that, for angular momentum $L\le N$, 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 generalisation of the usual superfluid one-vortex state to Bose-Einstein condensates in a trap.

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