Few-Body Quantum States and Interactions

当前理论极其有限的一类问题是，它对三到四个以上粒子的相互作用进行建模的能力，这些粒子可能是原子、分子、核子，甚至夸克。这项研究提出了一种最有希望的理论方法来攻击这一困难的类，该方法基于引入描述系统运动的不寻常的集体坐标。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，并提取准确的数值解。在达到精度之后，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，而且应该产生定性的见解，可以提出进一步推动研究领域的新途径。该项目还解决了修改维度对量子力学相互作用的影响，例如将三维气体挤压成煎饼状的二维几何图形或雪茄形状的一维几何图形。这种几何变化可以对少数粒子系统中发生的碰撞和束缚态产生戏剧性的影响。这项研究项目推进了目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，在创造新材料和开发化学过程方面，计算技术的进步在很大程度上能够进行，而不需要利用在最小规模下运行的新的量子力学定律。随着器件的小型化和材料在原子水平上微观控制的推进，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，这些技术使这种能力能够预测这种原子尺度系统的性质，并推动设计新类别量子系统的能力，使其能够在以前未曾预料到的方向上应用。这一努力还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库。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.