Annuaire

I am a researcher in mathematical physics, working in the group “dynamique quantique et nonlinéaire” at the ICB.

Research interests

My main research interest is the mathematical description of quantum mechanics, and its connections to functional analysis, partial differential equations, geometry and topology.

I am a co-organiser of the joint working seminar of the ICB and the mathematics institutes of Dijon (IMB) and Besançon (LMB).

Short Bio

After obtaining the diploma in mathematics at the university of Tübingen in 2010, I  wrote my PhD thesis under the supervision Stefan Teufel.

From 2014 to 2016 I worked as a postdoc with Mathieu Lewin at the universities of Cergy-Pontoise and Paris-Dauphine.

In 2016 I obtained a position for interdisciplinary research in mathematical physics at the CNRS.

• ANR MaBoP: Mathematical Analysis of the Bose Polaron
• EEQuaR: Effective equations in relativisc quantum mechanics.
• ANR DYRAQ on Dirac equations and relativistic quantum dynamics
• ANR QUACO on control of quantum systems
• I-QUINS on quantum information, within the I-SITE BFC excellence initiative

Preprints

• J.L and A. Triay: Validity of the Fröhlich model for a mobile impurity in a Bose-Einstein condensate; arxiv:2411.11655, 2024.
• J.L., and A. Triay: The excitation spectrum of a dilute Bose gas with an impurity in the Gross-Pitaevskii regime; arxiv:2401.14911, 2024.
• M. Falconi, J.L., D. Mitrouskas, and N. Leopold: Renormalized Bogoliubov Theory for the Nelson Model; arxiv:2305.06722, 2023.
• J. Kruse, and J.L., The Nelson Model on Static Spacetimes; arxiv:2109.00230, 2021.
• T. Binz, and J.L.: An abstract framework for interior-boundary conditions; arxiv:2103.17124, 2021.

Journal Articles

• J.L., M. Moscolari, S. Teufel, and T. Wessel: Equality of magnetization and edge current for interacting lattice fermions at positive temperature; Mathematical Physics Analysis and Geometry 27(24), 2024; arXiv:2403.17566.
• B. Hinrichs, and J.L.: A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate; Comptes Rendus Mathématqiue 362: 1399-1411, 2024; arXiv:2311.05361.
• J.L., D. Mitrouskas, and K. Mysliwy: On the global minimum of the energy-momentum relation for the polaron; Mathematical Physics Analysis and Geometry 26(17), 2023; arxiv:2206.14708.
  
• J.L.: Hamiltonians for polaron models with subcritical ultraviolet singularities. Annales Henri Poincaré 24:2687–2728, 2023; arXiv:2203.07253.
• J.L, L. Le Treust, S. Rota Nodari, and J. Sabin: The Dirac-Klein-Gordon system in the strong coupling limit. Annales Henri Lebesgue 6:541–573, 2023; arxiv:2110.09087.
• J.L., and P. Pickl: Dynamics of a tracer particle interacting with excitations of a Bose-Einstein condensate. Annales Henri Poincaré 23: 2855–2876, 2022; arXiv:2011.14428.
• J.L.: The resolvent of the Nelson Hamiltonian improves positivity. Mathematical Physics Analysis and Geometry 24(2), 2021; arxiv:2010.03235.
• J.L: The renormalised Bogoliubov-Fröhlich Hamiltonian. Journal of Mathematical Physics 61(10): 101902, 2020; arxiv:1909.02430.
• J. L.: A remark on the attainable set of the Schrödinger equation. Evolution Equations & Control Theory 10(3): 461-469, 2021; arxiv:1904.00591.
• V. Dorier, J.L., S. Guérin, and H.R. Jauslin: Canonical quantization for quantum plasmonics with finite nanostructures. Physical Review A 100, 2019; arXiv:1810.08014.
• J.L.: A nonrelativistic quantum field theory with point interactions in three dimensions. Annales Henri Poincaré 20(11), 2019; arxiv:1804.08295 .
• J.L., and J. Schmidt: On Nelson-type Hamiltonians and abstract boundary conditions. Communications in Mathematical Physics 367(2):629-663, 2019; arxiv:1803.00872
• S. Haag, J.L., and S.Teufel: Quantum waveguides with magnetic fields. Reviews in Mathematical Physics 31(8): 1950025, 2019; arXiv:1710.0151
• S. Haag, and J. L.: The adiabatic limit of the connection Laplacian. The Journal of Geometric Analysis 29(3): 2644–2673 , 2019; arXiv:1705.09801
• J. L., J. Schmidt, S. Teufel, and R. Tumulka, Particle Creation at a Point Source by Means of Interior-Boundary Conditions. Mathematical Physics Analysis and Geometry 21(2), 2018; arXiv:1703.04476
• S. Fournais, J.L., M. Lewin, and T. Østergaard Sørensen: Coulomb potentials and Taylor expansions in Time-Dependent Density Functional Theory. Rhysical Review A 93(6): 062510, 2016; arxiv:1603.02219
• J.L., and M. Lewin: Semi-classical Dirac vacuum polarisation in a scalar field. Annales Henri Poincaré 17(8): 1937-1954, 2016; arxiv:1506.00895
• J.L., and M. Lewin: A many-body RAGE theorem. Communications in Mathematical Physics 340(3): 1171-1186, 2015; arXiv:1503.00496
• J.L.: Convergence of nodal sets in the adiabatic limit. Annals of Global Analysis and Geometry 47(2): 147-166, 2015; arXiv:1405.1903
• S. Haag, J.L., and S. Teufel: Generalised Quantum Waveguides. Annales Henri Poincaré 16(11): 2535-2568, 2015; arXiv:1402.1067
• J.L., and S. Teufel: The adiabatic limit of Schrödinger operators on fibre bundles. Mathematische Annalen 367: 1647, 2017; arXiv:1402.0382

Conference Proceedings

• J.L., Ultraviolet Properties of a Polaron Model with Point Interactions and a Number Cutoff. In:  A. Michelangeli (Ed.), Mathematical Challenges in Zero Range Physics, Springer, 2021.HAL
• J.L., The BEC-polaron and the Bogoliubov-Fröhlich Hamiltonian. Oberwolfach Reports 16(3), 2019.
  
• J.L., Can quantum dynamics be described by the density alone? Oberwolfach Reports 13(3), 2016.
• J.L., S. Teufel: The adiabatic limit of the Laplacian on thin fibre bundles. In: D. Grieser, S. Teufel, A. Vasy (Eds.): Microlocal Methods in Mathematical Physics and Global Analysis, Birkhäuser, 2013.
• J.L., J. Wachsmuth, and S. Teufel: Effective Hamiltonians for thin Dirichlet tubes with varying cross-section. In: P. Exner (Ed.): Mathematical Results in Quantum Physics: Proceedings of the QMath11 Conference, World Scientific, 2011; arXiv:1011.3645

Habilitation Thesis: Mathematical results on many-body quantum systems, Université de Bourgogne, 2024; https://hal.science/tel-04769464

PhD Thesis: The adiabatic limit of Schrödinger operators on fibre bundles, Universität Tübingen, 2014

Diploma Thesis: The semi-classical Egorov theorem on Riemannian manifolds, Universität Tübingen, 2009

Spring 2025

Partial differential equations

In this course we study the theory of linear partial differential equations together with the necessary tools from functional analysis.

Lecture notes

Exercises (Adrien Tendani-Soler)

Sheet 1