# Small matrix path integral methods for quantum dynamics

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · University of Illinois at Urbana-Champaign (IL) · $600,000

## 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 organization:** 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

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2516676

## Citation

> US National Science Foundation, Award 2516676, Small matrix path integral methods for quantum dynamics. Retrieved via AI Analytics 2026-06-08 from https://api.ai-analytics.org/grant/nsf/2516676. Licensed CC0.

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