Few-Body Quantum States and Interactions

有一类问题，当前的理论是极其有限的，在它的能力，以模拟相互作用的三个或四个以上的粒子，可能是原子或分子或核子，甚至夸克。这项研究提出了一种最有前途的理论方法来解决这个困难的问题，这种方法是基于引入不寻常的集体坐标来描述系统的运动。一旦选择了最佳坐标，该项目就可以在现代计算机上实现量子力学方程，并提取精确的数值解。在达到精度后，对参数空间的后续探索不仅应该产生对新现象的可信预测，而且还应该产生定性的见解，可以提出进一步推进研究领域的新途径。该项目还处理了修改维度对量子力学相互作用的影响，例如将三维气体压缩成煎饼形状的二维几何形状或雪茄形状的一维几何形状。这种几何变化会对发生在少粒子系统中的碰撞和束缚态产生巨大影响。该研究项目推进了当前最重要的科学方向之一，即通过加深我们对原子、分子和光的量子力学行为的理解，并改善我们对这些系统的控制。几十年来，计算技术的进步，创造新材料的进步，化学过程的发展，已经能够在很大程度上不利用在最小尺度上运行的新量子力学定律。随着器件的日益小型化和材料在原子水平上的微观控制的推进，提高理论描述物质和光的量子力学行为的能力变得至关重要。该项目详细介绍了创建先进理论技术的计划，这些技术能够预测这种原子尺度系统的性质，并推动设计新型量子系统的能力，这些量子系统可以在以前意想不到的方向上应用。这一努力也加强了能够解决微观世界中最具挑战性的理论问题的人才储备。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

A class of problems where current theory is extremely limited is in its ability to model the interaction of more than three or four particles, which might be atoms or molecules or nucleons or even quarks. This research advances one of the most promising theoretical methods for attacking this difficult class, which is based on the introduction of unusual collective coordinates that describe the motions of the system. Once the best coordinates have been selected, the project can implement the quantum mechanical equations on modern computers, and extract accurate numerical solutions. Subsequent explorations of the parameter space after accuracy has been attained should yield not only credible predictions of new phenomena, but also qualitative insights that can suggest new paths that further advance the field of research. The project also tackles the effect of modified dimensionality on quantum mechanical interactions, such as squeezing a three-dimensional gas into a pancake-shaped two-dimensional geometry or a cigar-shaped one-dimensional geometry. Such geometrical changes can have a dramatic effect on the collisions and bound states that occur in a few-particle system.This research project advances one of the most vital scientific directions at present, namely, by deepening our understanding of the quantum mechanical behavior of atoms, molecules, and light, and improving our control of those systems. For decades, the progress in computing technology, in creating novel materials, in the development of chemical processes, has been able to proceed largely without utilizing the novel quantum mechanical laws that operate at the smallest scale. With increasing miniaturization of devices and advancing microscopic control of materials at the atomic level, it has become paramount to improve the capability of theory to describe the quantum mechanical behavior of matter and light. This project details plans to create advanced theoretical techniques that enable this ability to predict the properties of such atomic scale systems, and push forward capabilities for designing new classes of quantum systems that can enable applications in previously unanticipated directions. The effort also strengthens the pool of talent capable of tackling the most challenging theoretical questions in the microscopic world.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.