Analysis and Mathematical Physics

The research group studies the properties of effective evolution equations and justifies their validity as approximate descriptions of complex many-body quantum systems. Special emphasis is given to the derivation of mean-field and kinetic equations from the dynamics of fermionic systems and their interactions with the electromagnetic field.

• Norm approximation for the Fröhlich dynamics in the mean-field regime, N. Leopold, J. Funct. Anal. 285(4), 109979 (2023), DOI: 10.1016/j.jfa.2023.109979.
• 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), DOI: 10.1137/22M14936.
• Landau-Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron, N. Leopold, D. Mitrouskas, S. Rademacher, B. Schlein and R. Seiringer, Pure Appl. Anal. 3(4), 653-676 (2021), DOI: 10.2140/paa.2021.3.653.
• The Landau-Pekar equations: Adiabatic theorem and accuracy, N. Leopold, S. Rademacher, B. Schlein and R. Seiringer, Anal. PDE 14(7), 2079-2100 (2021), DOI: 10.2140/apde.2021.14.2079.
• Derivation of the Maxwell-Schrödinger Equations from the Pauli-Fierz Hamiltonian, N. Leopold and P. Pickl, SIAM J. Math. Anal. 52(5), 4900-4936 (2020), DOI: 10.1137/19M1307639.
• Derivation of the Time Dependent Gross-Pitaevskii Equation in Two Dimensions, M. Jeblick, N. Leopold and P. Pickl, Commun. Math. Phys. 372, 1–69 (2019), DOI: 10.1007/s00220-019-03599-x.