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Dr. Nikolai Leopold

Assistent/ PostDoc (FG Saffirio)

Spiegelgasse 1
4051 Basel



Since November 2021 I am a Marie Sklodowska-Curie Postdoctoral Fellow within the scope of the project Effective Equations for Fermionic Systems, supervised by Chiara Saffirio. Before that, I spent two years in the group of Chiara Saffirio at the University of Basel and two years in the group of 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. 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.

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

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,
to appear in Physics and the Nature of Reality: Essays in Memory of Detlef Dürr, arXiv:2304.12910.

Publications in peer-reviewed journals:

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:2203.03031.

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, DOI: 10.1007/978-3-030-01602-9, 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:

19. Effective dynamics for the Nelson model with many fermions,
contribution to the mini-workshop report "Lorentz Gas Dynamics: particle systems and scaling limits" (2019), DOI: 10.4171/OWR/2019/10

18. Derivation of the Maxwell-Schrödinger Equations from the Pauli-Fierz Hamiltonian
contribution to the workshop report "Mathematical Questions and Challenges in Quantum Electrodynamics and its Applications" (2017), DOI: 10.4171/OWR/2017/41.