Through a better understanding of atomic interactions, we hope to enable, to motivate, and to build a better understanding of the world around us as a quantum system of many atoms.
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.
As physicists, we do not make any statement lightly. Every statement above has reasons and arguments behind it that we hope to expand upon later, on this page and/or in publications. We hope also to understand and explain the following.
One more point:
We are trying to better understand the relation between interaction and complexity. Here is an initial effort. It explains why we expect systems with repulsive inter-particle interactions to remain "simple" despite interaction.
We will have more works on complexity.
More to be done even after much effort over many years (see Publications)
Initial work from many years ago:
Our efforts on few-atom and many-atom systems have stalled for many years, partly due to the lack of resources and partly due to our belief that the two-body interaction needs to be better understood first for further significant progress in those areas.
Subsequent works on reactions are related:
There are also many related works in the community, some of which we hope to have helped to stimulate, on studies of van der Waals universality in few-body physics. One can look for works by the group of Paul Julienne and the group of Chris Greene, among others.
Much more to be done and understood.
Initial work from many years ago:
Much more to be done, and we hope to revisit it soon.
Home | Research | Publications | Quantum Mechanics | Bio