Quantum Theories of Fundamental Atomic and Molecular Interactions

这个项目的重点是在广泛的能量范围内改进原子和/或分子之间相互作用的理论描述。这些基本的相互作用是贯穿物理和化学的量子多体系统研究的基本成分，并且越来越多地应用于生物学和生命科学。在量子力学对复杂多体系统的大多数应用中，出于实用性和权宜之计，原子和/或分子之间的双向相互作用近似于简单的分析形式，但忽略了基本的物理学。相比之下，通过精确的第一性原理计算来更好地表达这些相互作用，太复杂了，无法纳入多体研究。这个项目是解决这个难题的努力的一部分，并发展基本原子相互作用的量子理论，这些理论既简单又系统，可以纳入量子多体理论，同时又足够精确，可以捕捉所有基本的物理现象。实现这一目标的程度可能决定多体系统的理论模型和模拟与现实世界实验观测的相关性。该项目建立在最近成功的原子-原子和离子-原子相互作用量子缺陷理论的基础上。它打算将它们应用于为多原子系统开发更好的模型，并将它们扩展到其他基本的原子相互作用，如电子-原子相互作用。量子缺陷理论是关于结构和相互作用的一般理论，它利用了这样一个事实，即在大多数感兴趣的能量范围内，原子相互作用的复杂性，例如它们的能量和部分波依赖性，几乎完全是由于远程相互作用，这使得它们适合于系统的和经常分析的处理。该项目还打算采取初步步骤，发展各向异性相互作用的量子缺陷理论，如原子-分子相互作用，最终目标是为原子和分子结构和相互作用的各个方面实现统一和有效的框架。

This project is focused on improved theoretical descriptions of the interactions between atoms and/or molecules over a broad range of energy. These elementary interactions are the essential ingredients for the study of quantum many-body systems throughout physics and chemistry, and, increasingly, in biology and the life-sciences as well. In most applications of quantum mechanics to complex many-body systems, the pairwise interactions between atoms and/or molecules are approximated with simple analytical forms dictated by practicality and expedience, but which neglect essential physics. Better representations of these interactions through accurate, first-principle calculations, by contrast, are simply too complicated to incorporate into many-body studies. This project is part of an effort to resolve this conundrum and to develop quantum theories of fundamental atomic interactions that are both sufficiently simple and systematic to be incorporated into quantum many-body theories, and simultaneously accurate enough to capture all the essential physics. The degree to which this can be accomplished may well determine the relevance of theoretical models and simulations of many-body systems to real-world experimental observations. The project builds on the recent success of quantum defect theories for atom-atom and ion-atom interactions. It intends both to apply them to develop better models for many-atom systems, and to extend them to other fundamental atomic interactions such as the electron-atom interaction. Quantum defect theories are general theories of structures and interactions that take advantage of the fact that over most energy ranges of interest, the complexities in atomic interactions, such as their energy and partial wave dependences, are due almost entirely to the long-range interaction, which makes them amenable to systematic and often analytic treatment. The project also intends to take initial steps towards the developments of quantum defect theories for anisotropic interactions, such as the atom-molecule interaction, with the ultimate goal of achieving a unified and an efficient framework for all aspects of atomic and molecular structures and interactions.