Collective modes of a harmonically trapped one-dimensional Bose gas: the effects of finite particle number and nonzero temperature

Following the idea of the density functional approach, we develop a generalized Bogoliubov theory of an interacting Bose gas confined in a one-dimensional harmonic trap, by using a local chemical potential - calculated with the Lieb-Liniger exact solution - as the exchange energy. At zero temperature, we use the theory to describe collective modes of a finite-particle system in all interaction regimes from the ideal gas limit, to the mean-field Thomas-Fermi regime, and to the strongly interacting Tonks-Girardeau regime. At finite temperature, we investigate the temperature dependence of collective modes in the weak-coupling regime by means of a Hartree-Fock-Bogoliubov theory with Popov approximation. By emphasizing the effects of finite particle number and nonzero temperature on collective mode frequencies, we make comparisons of our results with the recent experimental measurement [E. Haller et al., Science 325, 1224 (2009)] and some previous theoretical predictions. We show that the experimental data are still not fully explained within current theoretical framework.Comment: 10 pages, 8 figure

Light-Cone Sum Rules Analysis of ΞQQ′q→ΣQ′∗\Xi_{QQ^{\prime}q}\to\Sigma_{Q^{\prime}}^{*} Weak Decays

In this work, we investigate the semi-leptonic weak decays of spin-1/2 doubly-heavy baryons $\Xi_{QQ^{\prime}}$ into spin-3/2 singly-heavy baryons $\Sigma_{Q^{\prime}}^*$ within light-cone sum rules. Using the parallel components of the light-cone distribution amplitudes of $\Sigma_{Q^{\prime}}^*$, the transition form factors for these decays are calculated both analytically and numerically. The numerical results for these semi-leptonic weak decays widths and branching ratios are also predicted, which are compared with the same predictions by other theoretical approaches in the literatures. These phenomenology predictions can be tested by the experiments in the future.Comment: 19 pages, 2 figures, 4 table