Few-Body Quantum States and Interactions

Purdue University, West Lafayette IN

Investigators

Abstract

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.