Universal and Non-Universal Few-Body Physics in the Ultracold

自量子力学早期以来，少体物理学在原子、分子和核物理学中发挥了突出的作用。计划对超冷s波与至多六个粒子的原子少体系统的普适和非普适方面进行微观描述。具体来说，超球显式相关高斯方法（HECG）适用于四体和五体系统有限的轨道角动量将开发。与“标准”显式相关高斯方法一起，这种方法将被应用到具有各种对称性和大的s-波散射长度的少原子系统。此外，将研究周期结构（周期盒或光学晶格）中的少体系统的物理学。最后，将开发和应用微观有限温度的方法。预计算法的发展将对物理和化学中的各种分支学科产生影响。HECG方法的成功推广到有限角动量的状态，预计将提供单通道和多通道散射观测。因此，所开发的方法除了在原子和分子物理学中的应用之外，还可以在核和化学物理学中找到应用。在超冷少体系统中的应用将大大增强我们对基本但高度相关的少体态的理解，这些少体态支配着超冷量子气体的大部分动力学。学生将积极参与拟议研究活动的各个方面，包括基础研究的规划，计算以及结果的解释和异议。本科生和研究生在原子理论方面的研究培训，重点是分析和数值技术，为他们将来的各种追求做好准备。学生的课堂体验将通过结合一些最新的进展得到改善。

Few-body physics has played a prominent role in atomic, molecular and nuclear physics since the early days of quantum mechanics. A microscopic description of universal and non-universal aspects of ultracold s-wave interacting atomic few-body systems with up to six particles is planned. Specifically, a hyperspherical explicitly correlated Gaussian approach (HECG) applicable to four- and five-body systems with finite orbital angular momentum will be develoepd. Together with the "standard" explicitly correlated Gaussian approach, this approach will be applied to few-atom systems with various symmetries and large s-wave scattering lengths. Moreover, the physics of few-body systems in periodic structures (a periodic box or an optical lattice) will be investigated. Lastly, microscopic finite-temperature approaches will be developed and applied.The algorithm developments are expected to have implications for a variety of subdisciplines within physics and chemistry. The successful generalization of the HECG approach to states with finite angular momentum is expected to provide access to single- and multi-channel scattering observables. As such, the developed approach may find applications in nuclear and chemical physics, in addition to applications in atomic and molecular physics. The applications to ultracold few-body systems will significantly enhance our understanding of fundamental, yet highly correlated, few-body states, which govern much of the dynamics of ultracold quantum gases. Students will be actively involved in all aspects of the proposed research activities including the planning of the fundamental studies, the calculations and the interpretation and dissimination of the results. The research training of undergraduate and graduate students in atomic theory with emphasis on analytical and numerical techniques prepares them for a wide variety of future pursuits. Students' classroom experiences will be improved by incorporating some of the latest advances.