Analytical results for trapped weakly interacting bosons in two dimensions - art. no. 013602

摘要

We consider a model of N two-dimensional bosons in a harmonic trap with translational and rotational invariant, weak two-particle interaction. We present in configuration space a systematical recursive method for constructing all wave functions with angular momentum L and corresponding energies and apply it to L less than or equal to 6 for all N. The lower and the upper bounds for interaction energy are estimated. We analytically confirm the conjecture of Smith et al. that the elementary symmetric polynomial is the ground state for repulsive delta interaction for all N greater than or equal to L up to L less than or equal to 6, Additionally, we find that there exist vanishing-energy solutions for L greater than or equal to N(N-1), signaling the exclusive statistics. Finally, we consider briefly the case of attractive powerlike potential r(k), k > -2, and prove that the lowest-energy state is still the one in which the whole angular momentum is absorbed by the center-of-mass motion. [References: 22]