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.

• The Semi-Classical Limit from the Dirac Equation with Time-Dependent External Electromagnetic Field to Relativistic Vlasov Equations
  F. Golse, N. Leopold, N.J. Mauser, J. Möller, and C. Saffirio,
  Preprint, arXiv:2512.17849.
• Φ^4_2 theory limit of a many-body bosonic free energy
  L. Jougla and N. Rougerie,
  Preprint, arXiv:2512.10704.
• Derivation of the Maxwell-Schrödinger and Vlasov–Maxwell Equations from Non-Relativistic QED 
  N. Leopold,
  Preprint, arXiv:2411.07085.
• Derivation of the Vlasov-Maxwell system from the Maxwell-Schrödinger equations with extended charges
  N. Leopold and C. Saffirio,
  accepted for publication in Forum of Mathematics Sigma, arXiv:2308.16074.
• Ground state of Bose gases interacting through singular potentials
  L. Boßmann, N. Leopold, S. Petrat, and S. Rademacher,
  J. Funct. Anal. 111268 (2025), DOI: 10.1016/j.jfa.2025.111268,
• Renormalized Bogoliubov Theory for the Nelson Model
  M. Falconi, J. Lampart, N. Leopold, and D. Mitrouskas,
  Ann. Inst. H. Poincaré C Anal. Non Linéaire, published online first (2025), DOI: 10.4171/AIHPC/154, arXiv:2305.06722.