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Dr. Nikolai Leopold

Assistent/ PostDoc (FG Saffirio)

Spiegelgasse 1
4051 Basel



Since November 2019 I have been a postdoctoral researcher in the group of Chiara Saffirio. Over the last two years my research has been supported by a Marie Sklodowska-Curie Postdoctoral Fellowship within the scope of the project Effective Equations for Fermionic Systems. Prior to this, I spent two years in the research group led by Robert Seiringer at the Institute of Science and Technology Austria. I obtained my Ph.D. in mathematics at the LMU Munich under the supervision of Peter Pickl.

My field of research is mathematical physics. In particular, I am applying tools from functional analysis, partial differential equations and semiclassical analysis to study the properties of effective evolution equations and to derive them from many-body quantum mechanics.



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

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

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


14. A Note on the Binding Energy for Bosons in the Mean-field Limit,
L. Boßmann, N. Leopold, D. Mitrouskas and S. Petrat, J. Stat. Phys. 191, 48 (2024),

13. 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 (2024),

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

11. 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.

10. 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.

9. Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model,
M. Falconi, N. Leopold, D. Mitrouskas and S. Petrat, Rev. Math. Phys. 35(4), 2350006 (2023), arXiv:2110.00458.

8. 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), arXiv:2005.02098.

7. Derivation of the Landau-Pekar equations in a many-body mean-field limit,
N. Leopold, D. Mitrouskas and R. Seiringer, Arch. Ration. Mech. Anal. 240, 383--417 (2021), arXiv:2001.03993.

6. The Landau-Pekar equations: Adiabatic theorem and accuracy,
N. Leopold, S. Rademacher, B. Schlein and R. Seiringer, Anal. PDE 14(7), 2079--2100 (2021), arXiv:1904.12532

5. Theory of the Rotating Polaron: Spectrum and Self-Localization,
E. Yakaboylu, B. Midya, A. Deuchert, N. Leopold and M. Lemeshko, Phys. Rev. B  98, 224506 (2019), DOI: 10.1103/PhysRevB.98.224506, arXiv:1809.01204.

4. Mean-Field Dynamics for the Nelson Model with Fermions,
N. Leopold and S. Petrat, Ann. Henri Poincaré  20, 3471–3508 (2019), DOI: 10.1007/s00023-019-00828-w, arXiv:1807.06781.

3. Mean-field limits of particles in interaction with quantized radiation fields
N. Leopold and P. Pickl, in: Cadamuro, D., Duell, M., Dybalski, W., Simonella, S. (eds) Macroscopic Limits of Quantum Systems, MaLiQS 2017, Springer Proceedings in Mathematics & Statistics 270, Springer, Cham (2018), , arXiv:1806.10843.

2. 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, arXiv:1609.01545.

1. 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, arXiv:1608.05326.

Contributions to Oberwolfach Reports:

20. Mini-Workshop: Mathematics of Many-body Fermionic Systems,
N. Leopold, P.T. Nam and C. Saffirio,
Oberwolfach Rep. 49/2023 (preliminary version), DOI: 10.14760/OWR-2023-49.

19. Effective dynamics for the Nelson model with many fermions,
contribution to the mini-workshop report 10/2019 "Lorentz Gas Dynamics: particle systems and scaling limits", DOI: 10.14760/OWR-2019-10.

18. Derivation of the Maxwell-Schrödinger Equations from the Pauli-Fierz Hamiltonian
contribution to the workshop report 41/2017 "Mathematical Questions and Challenges in Quantum Electrodynamics and its Applications", DOI: 10.14760/OWR-2017-41.