Model Reduction Methods for Extended Quantum Systems: Analysis and Applications

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Much recent development in materials science and chemistry involves quantum properties of the underlying systems. Quantum properties are often studied as if the system of interest is isolated and evolves by itself, but in practice, a quantum system is always coupled with its surrounding environment. Direct simulations of such a system can result in overwhelming computational costs. There is a strong demand for simplified models and efficient simulation algorithms so that people can study quantum systems - such as semiconductors and nanoelectronic devices - while retaining realistic complexity. This project tackles the fundamental challenge of simulating an extended system with quantum degrees of freedom by developing new models and data-assimilation methods. The project will provide research training opportunities for undergraduates.This project will focus on a Galerkin-projection-based model-reduction framework. This project will aim to separate the quantum system from its surrounding environment and describe the dynamics with fewer variables. This project will provide rigorous error analysis of the model-reduction method and consider a nonparametric data-driven approach to estimate the system properties from data observations. As an interdisciplinary project, this project will bridge techniques from different disciplines, including mathematics, physics, chemistry, and quantum computing, and give rise to more accurate and reliable models that can be implemented to accelerate computationally heavy problems of different disciplines.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.