中文摘要：

借用密度泛函方法并结合局域密度近似和Bethe ansatz精确解结果,研究了玻色费米混合物及旋量玻色气体在束缚于一维简谐外势下时各分量的混合与相分离。结果表明,玻色费米混合物会随着玻色-玻色、玻色-费米原子间排斥相互作用的增强,出现费米子被排斥在势阱中心之外的玻色费米部分相分离现象,当排斥相互作用趋于无限强时,玻色费米混合物的基态能量和总密度与所有原子都费米化的情况相一致;自旋-1玻色气体在密度-密度排斥和反铁磁自旋交换相互作用下会出现配对玻色子和极化玻色子相分离的现象,在强作用下,各自的密度分布曲线分别趋近于玻色-玻色对的TG气体和标量玻色TG气体,而中心密度随相互作用强度的变化呈非单调性。

英文摘要：

By density functional theory combined with the local density approximation and Bethe ansatz exact solution,this paper studies the mixing and phase separation of components for Bose-Fermi mixture and spinor Bose gas in the one dimensional harmonic traps.For Bose-Fermi mixture,the results show that at sufficiently strong interaction,a considerable amount of fermions are repelled out of the central region of the trap,exhibiting partial phase separation of Bose and Fermi components.At infinitely strong interaction,the ground-state energy of the mixture and the total density are consistent with the scenario that all atoms in the mixture are fully fermionized.For spin-1bosons with repulsive density-density interaction and anti-ferromagnetic spin-exchange interaction,the results reveal the phase separation of the paired and polarized bosons,the density profiles of which respectively approach the Tonks-Girardeau gases of Bose-Bose pairs and scalar bosons in the case of strong interaction.