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

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

2000-02-24

arxiv.org/abs/cond-mat/0002381v1

Phys. Lett. A, 267 p. 416 (2000)

Physics

Condensed Matter

Statistical Mechanics

6 pages, no figures, accepted for publication on Physics Letters A

Scientific paper

10.1016/S0375-9601(00)00123-7

The fact that the ground-state first-order density matrix for Bosons in a parabolic potential with interparticle harmonic interactions is known in exact form is here exploited to study collective excitations in the weak-coupling regime. Oscillations about the ground-state density are treated analytically by a linearized equation of motion which includes a kinetic energy contribution. 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 renormalized by the interactions.

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