Small matrix path integral methods for quantum dynamics

NSF Award Search · 01002526DB NSF RESEARCH & RELATED ACTIVIT · $600,000 · view on nsf.gov ↗

Abstract

Supported by the Chemical Theory, Models and Computational Methods program in the Division of Chemistry, Nancy Makri of the University of Illinois at Urbana-Champaign is to develop accurate and efficient real-time path integral methods for simulating quantum mechanical processes in large environments. Quantum mechanics governs the interactions among electrons and nuclei, giving rise to complex and subtle dynamics that dictate the outcome of processes of immense importance to biology, energy harvest, and quantum computers. Understanding and controlling such phenomena hinges on the availability of accurate and robust simulation tools. Traditional approaches are hindered by the infamous scaling of the quantum mechanical equations, whose solution requires computational effort that increases exponentially with the number of particles. Makri’s approach is based on Feynman’s path integral formulation of quantum mechanics, which circumvents this issue by avoiding the explicit calculation of wave functions. However, the path integral encounters other severe computational obstacles, such as numerical instabilities and astronomical numbers of terms that must be included. Makri has developed a small matrix path integral (SMatPI) methodology that overcomes these problems in many important situations. She will further develop this approach, to increase its efficiency and make it suitable for simulating processes of increased complexity. A broader impact of this work will be the development

Key facts

NSF award ID
2516676
Awardee
University of Illinois at Urbana-Champaign (IL)
SAM.gov UEI
Y8CWNJRCNN91
PI
Nancy Makri
Primary program
01002526DB NSF RESEARCH & RELATED ACTIVIT
All programs
Software Institutes, ADVANCED SOFTWARE TECH & ALGOR, COMPUTATIONAL SCIENCE & ENGING
Estimated total
$600,000
Funds obligated
$600,000
Transaction type
Standard Grant
Period
09/01/2025 → 08/31/2028