Dr. Nikolai Leopold
Assistent/ PostDoc (FG Saffirio)
Office
Spiegelgasse 1
4051 Basel
Switzerland
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.
Publications
Preprints:
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.
Publications:
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), https://doi.org/10.1007/s10955-024-03260-5, arXiv:2307.13115.
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), https://doi.org/10.1007/978-3-031-45434-9_22, arXiv:2304.12910.
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), https://doi.org/10.1007/978-3-030-01602-9_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:
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.