https://doi.org/10.1140/epjd/e2004-00055-9
Sum-rule approaches to the elementary excitation spectrum of interacting gases of finite bosons in harmonic potentials
Department of Physics, Fudan University, Shanghai 200433,
P.R. China
Corresponding author: a ylma@fudan.ac.cn
Received:
20
May
2003
Revised:
18
February
2004
Published online:
20
April
2004
Based on the corrected sum rules and generalized virial identities, we
derive an expression for all modes of excitation spectrum of interacting
Bose gases at finite atom numbers in axially anisotropic potentials, in
terms of the N-body ground state average. Using the variational Gaussian
calculation for the ground-state wave function, its explicit analytic
formulas are obtained. These results show clearly the dependence of
excitation spectrum on the interaction strength parameter 
and trap geometry parameter 
for the system with N=1 through 
. For 
and 1 the dependences have simple and intuitive physical
interpretations. We compare the low-lying excitation spectra with the
existing numerical results and make quantitative predications for future
experiments and numerical simulation for higher-lying excitation modes.
PACS: 67.40.Db – Quantum statistical theory; ground state, elementary excitations / 67.90.+z – Other topics in quantum fluids and solids; liquid and solid helium
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2004
