During my Ph.D., I contributed to several publications, some of which are currently under review. In addition, I have prepared manuscripts that will be submitted to journals in the near future.
My favourite Results are:
New Bounds on the Maximal Excess Charge of Atoms in [4]
The Absence of the Efimov Effect in a System of Confined Particles in [5]
The lists below include papers, preprints, and manuscripts that I have authored or co-authored. For details on current and upcoming projects, please refer to my research statement.
[1] The sharp one-dimensional Lieb-Thirring inequality for the sum of eigenvalues Larry Read and M.R. Schulz
Use of AI for the result above [1]: The arguments in the preprint above have been found under guidance of L.R. and M.R.S. Please see the more detailed use of AI statement in the preprint on the arXiv. The authors take full responsibility for the final version of the proof.
[2] An Improved Nonexistence Bound for the Liquid Drop Model M.R. Schulz
[3] On the Efimov Effect for Four Particles in Dimension Two J. Rau and M.R. Schulz
[4] On The Excess Charge Problem of Atmos D. Hundertmark, N. Pattakos and M.R. Schulz
An additional Supplement is available on ResearchGate.
[5] Why a System of Three Bosons on Separate Lines Can Not Exhibit the Confinement Induced Efimov Effect D. Hundertmark, M.R. Schulz, S. Vugalter
Published Papers
[6] Absence of the confinement–induced Efimov effect: a direct proof in a specific geometry M.R. Schulz, S. Zalczer
Schulz, M.R., Zalczer, S. Absence of the confinement–induced Efimov effect: a direct proof in a specific geometry. Lett Math Phys 115, 135 (2025). https://doi.org/10.1007/s11005-025-02019-7
The following are published papers that I completed during the last six months of my Master’s studies, while working on a MathSEE project at KIT and before starting my Ph.D. position. Publication [Phys 1] was primarily written by me, whereas for [Phys 2] I contributed by suggesting approaches to certain differential equations and was subsequently invited to join as a co-author. Contrary to mathematics standards and as usual for physics publications, the order of authors is given regarding their relevance for the result.
[7, Phys 1] Analytical Solution of a Gas Release Problem Considering Permeation With Time-dependent Boundary Conditions
Marvin R. Schulz, Kaori Nagatou, Axel von der Weth, Frederik Arbeiter and Volker Pasler. Journal of Computational and Theoretical Transport, 49(7), 389–412.
[8, Phys 2] Numerical Analysis of an Isovolumetric Thermal Desorption Experiment
Weth, Axel von der, Frederik Arbeiter, Kaori Nagatou, Volker Pasler, Dmitri Klimenko, and Marvin Schulz. Diffusion Foundations, 27, 122-135.