Few-Body Quantum States and Interactions

当前理论极其有限的一类问题是，它能够模拟三个或四个以上粒子的相互作用，这些粒子可能是原子或分子或核子，甚至是夸克。 这项研究提出了一个最有前途的理论方法来攻击这个困难的类，这是基于引入不寻常的集体坐标，描述系统的运动。 一旦选定了最佳坐标，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。 在达到精确度后，对参数空间的后续探索不仅应该产生对新现象的可靠预测，而且还应该产生定性的见解，这些见解可以提出进一步推进研究领域的新途径。 该项目还解决了修改的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形状或雪茄状的一维几何形状。 这样的几何变化会对少粒子系统中的碰撞和束缚态产生巨大的影响。本研究项目将深化对原子、分子和光的量子力学行为的理解，提高对这些系统的控制能力，从而推进当前最重要的科学方向之一。 几十年来，计算技术的进步，创造新材料，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在原子水平上推进材料的微观控制，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的理论技术的计划，这些技术能够预测这种原子尺度系统的特性，并推动设计新型量子系统的能力，这些系统可以在以前未预料到的方向上实现应用。 该奖项反映了NSF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.