Non-Perturbative Analysis of Physical and Mathematical Models

Ohio State University, The, Columbus OH

Investigators

Abstract

In modeling the natural world, scientists often must rely on approximations that result in incomplete information about a system under study. Such is the case in elementary particle physics, statistical mechanics, and gravitation. A fundamental question is then how to extract from limited data as much information as possible, with the possible highest level of accuracy and confidence. This project will draw on several areas of mathematics to analyze this issue in mathematics and physics. Additionally, the investigator aims to further develop the mathematics of laser-matter interaction. The project offers training research opportunities for graduate students. A central topic addressed in the project is the interaction of matter and radiation. For the time-dependent laser-induced photoelectric effect, the investigator will apply a constructive mathematical technique to the photoionization models and the two-frequency models used in experiments, to fine-tune the photoelectric output and, in interdisciplinary work with experimentalists, to predict and optimize the processes. A second aim of the project is to determine the behavior of physical and mathematical models outside the range of perturbation theory, with the highest possible level of accuracy and confidence, when only a limited number of terms of a perturbation expansion can be calculated. The investigator aims to develop methods that exceed the precision previously achieved and that are optimal under specific mathematical conditions. The methods will be applied also to mathematical problems in which exact solutions are available, but their numerical utilization is computationally demanding. 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.