Mathematical model and computational implementation of open quantum systems for molecular simulations

• Applicant: Professor Dr. Luigi Delle Site
• Subject Area: Mathematics ; Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics ; Theoretical Condensed Matter Physics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 541471810

First-principles models of atomic and molecular systems formalized in the language of mathematics and implemented in efficient simulation codes represent powerful predictive tools. Independently, requirements of accuracy and reproducibility of modern experimental and technological research call for the systematic translation of complex mathematical models into the related computational techniques and simulation codes. Yet, persistent obstacles to the constructive co-development of mathematical models and their computer implementations remain in the form of substantial differences between the scientific languages and short-term goals of the participating disciplines. Numerical analysis and statistics are gaining importance in these developments by providing robust algorithms and advanced methods for the interpretation of the simulation data, but mathematics is not involved as systematically as it could (and should) be so far. This proposal aims to help narrowing this gap through the development of a rigorous mathematical model of open molecular system with quantum/electronic degrees of freedom, and to systematically implement it in the well-established adaptive resolution simulation code framework. The resulting code for open systems will be applicable, and applied, to quantum/electronic calculations that cannot be efficiently performed with current simulation tools. The code should be openly available and user-friendly to users and potential future contributors of applied and theoretical community.

• DFG Programme: Research Grants