Using two different numerical methods, we study the behavior of two-component Fermi gases interacting through short-range s-wave interactions in a harmonic trap. A correlated Gaussian basis-set expansion technique is used to determine the energies and structural properties, i.e., the radial one-body densities and pair distribution functions, for small systems with either even or odd $N$, as functions of the s-wave scattering length and the mass ratio $κ$ of the two species. Particular emphasis is put on a discussion of the angular momentum of the system in the BEC-BCS crossover regime. At unitarity, the excitation spectrum of the four-particle system with total angular momentum L=0 is calculated as a function of the mass ratio $κ$. The results are analyzed from a hyperspherical perspective, which offers new insights into the problem. Additionally, fixed-node diffusion Monte Carlo calculations are performed for equal-mass Fermi gases with up to N=30 atoms. We focus on the odd-even oscillations of the ground state energy of the equal-mass unitary system having up to N=30 particles, which are related to the excitation gap of the system. Furthermore, we present a detailed analysis of the structural properties of these systems.
Correlation effects in the ground state of trapped atomic Bose gases
研究了囚禁超冷原子玻色气体中的多体关联效应。我们使用基态辅助场量子蒙特卡罗（QMC）方法[Phys. Rev. E 70，056702（2004）]计算气体的基态。我们研究气体的性质，如能量，冷凝分数，真实空间密度和动量分布，作为粒子数量和散射长度的函数。我们发现，平均场Gross-Pitaevskii（GP）方法给出的动能作为散射长度的函数的定性错误的结果。我们提出了详细的QMC数据的各种数量，并讨论了GP的行为，修改GP，和Bogoliubov方法下的局部密度近似。
Equilibrium Properties of Trapped Dipolar Gases at Finite Temperatures
研究了有限温度下偶极玻色和费米气体的平衡性质。我们最近发展了有限温度下偶极费米气体相空间分布函数的变分分析。我们扩展的变分形式主义玻色气体和讨论的偶极相互作用与不同的统计热平衡的效果，特别强调在动量空间的变形。我们通过改变温度、陷阱纵横比和偶极矩来研究系统的稳定性。此外，我们讨论了如何在高温状态下观察到真实空间和动量空间中的变形，这与JILA [Ni et al. Science 322，231（2008）]和东京大学[Aikawa et al. New. 11，055035（2009）]。
