Roles of Collective Excitations in the Anomalous Fluctuations of One-Dimensional Interacting Bose-Condensed Gases

The particle-number fluctuations due to collective excitations are calculated for a one-dimensional interacting Bose-condensed gas confined in a harmonic potential. By using the Thomas-Fermi
approximation, the behaviour of the anomalous fluctuations is found to be <δ²N₀> ～ N^10/3/( ln N)² with N being the total number of particles.