Collective excitation frequencies of bosons in a parabolic potential with interparticle harmonic interactions

The fact that the ground-state first-order density matrix for bosons in a p arabolic potential with interparticle harmonic interactions is known in exa ct form is here exploited to study collective excitations in the weak-coupl ing regime. Oscillations about the ground-state density are treated analyti cally by a linearized equation of motion which includes a kinetic energy co ntribution. We show that the dipole mode has the frequency of the bare trap , in accord with the Kohn theorem, and derive explicit expressions for the frequencies of the higher-multipole modes in terms of a frequency renormali zed by the interactions. (C) 2000 Elsevier Science B.V. All rights reserved .