Effective Equations for Fermionic Systems


Researcher:  Nikolai Leopold
Supervisor:  Chiara Saffirio

Project Overview:

Type of project: Marie Sklodowska-Curie Individual Fellowship
Acronym: EFFECT
Project number: 101024712
Start date: 01.11.2021
End date:  14.11.2023

Short Description:

Fermionic systems play a significant role in the description of molecules and condensed matter. Their time evolution is determined by the Schrödinger equation which, however, is very challenging to analyze in the presence of many particles. For this reason simpler but less exact effective equations are used to approximately predict the time evolution. In the scope of this project new mathematical tools will be developed to rigorously justify the use of effective equations for large fermionic systems and to prove their range of validity. This will enhance the understanding of the non-equilibrium dynamics of fermionic systems and their interaction with the electromagnetic field.

Preprints and publications which has received funding from the project:

Ground state of Bose gases interacting through singular potentials,
L. Boßmann, N. Leopold, S. Petrat and S. Rademacher, Preprint, arXiv:2309.12233.

Derivation of the Vlasov-Maxwell system from the Maxwell-Schrödinger equations with extended charges
N. Leopold and C. Saffirio, Preprint, arXiv:2308.16074.

A Note on the Binding Energy for Bosons in the Mean-field Limit,
L. Boßmann, N. Leopold, D. Mitrouskas and S. Petrat, Preprint, arXiv:2307.13115.

Renormalized Bogoliubov Theory for the Nelson Model,
M. Falconi, J. Lampart, N. Leopold and D. Mitrouskas, Preprint, arXiv:2305.06722.

Asymptotic analysis of the weakly interacting Bose gas: A collection of recent results and applications,
L. Boßmann, N. Leopold, D. Mitrouskas and S. Petrat, in: Bassi, A., Goldstein, S., Tumulka, R., Zanghi, N. (eds), Physics and the Nature of Reality. Fundamendal Theories of Physics, vol. 215. Springer, Cham. https://doi.org/10.1007/978-3-031-45434-9_22arXiv:2304.12910 (2024).

Norm approximation for the Fröhlich dynamics in the mean-field regime
N. Leopold, J. Funct. Anal. 285(4), 109979 (2023), arXiv:2207.01598.

Derivation of the Maxwell-Schrödinger Equations: A note on the infrared sector of the radiation field
M. Falconi and N. Leopold, J. Math. Phys. 64, 011901 (2023), arXiv:2203.16368.

Propagation of moments for large data and semiclassical limit to the relativistic Vlasov equation
N. Leopold and C. Saffirio, SIAM J. Math. Anal. 55(3), 1676--1706 (2023), arXiv:2203.16368.


This project is funded by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement N° 101024712.