Mathematical Physics: My research uses mathematical analysis to investigate problems motivated by quantum physics. I primarily employ tools from operator theory, matrix analysis, probability, spectral theory, and perturbation theory. Recent topics include:
Quantum dynamics and transport: velocity bounds and transport suppression in periodic and disordered systems.
(Disordered) many-body systems: many-body localization, entanglement area laws, entanglement dynamics, Lieb-Robinson bounds and decay of correlations.
My work is multidisciplinary and centers on models relevant in quantum information theory and condensed matter physics, with promising applications in Physics and Computer science/engineering.
Christopher Cedzich, FernUniversität in Hagen, Germany
Jake Fillman, Texas A&M, USA
Christoph Fischbacher, Baylor University, USA
Marius Lemm, University of Tübingen, Germany
Wencai Liu, Texas A&M, USA
Angelo Lucia, Politecnico di Milano, Italy
Bruno Nachtergaele, University of California, Davis, USA
Robert Sims, University of Arizona, USA
Günter Stolz, University of Alabama at Birmingham, USA
Amanda Young, University of Illinois Urbana-Champaign, USA
Albert H. Werner, University of Copenhagen, Denmark
Exponential suppression of transport in periodic electric quantum walks (with M. Cedzich, G. Stolz, and A. H. Werner),
Preprint- arXiv: 2511.15664
Sharp polynomial velocity decay bounds for multidimensional periodic schrödinger operators (with J. Fillman, C. Fischbacher, and W. Liu),
Preprint- arXiv: 2509.04381
Entanglement bounds for single-excitation energy eigenstates of quantum oscillator systems (with R. Sims and G. Stolz),
Letters in Mathematical Physics, 114, 116 (2024)- arXiv | Journal
Slow propagation velocities in Schrödinger operators with large periodic potential (with M. Darras, C. Fischbacher, and G. Stolz), Annales Henri Poincaré 26 (2025), 3635–3663. - arXiv| Journal
Exponentially decaying velocity bounds of quantum walks in periodic fields (with G. Stolz),
Communications in Mathematical Physics 403 (2023), 1297-1327. arXiv| Journal
Dynamical Evolution of Entanglement in Disordered Oscillator Systems,
Reviews in Mathematical Physics 35 (2023) 2350003 (32 pages) . arXiv| Journal
Entanglement bounds in the XXZ quantum spin chain (with C. Fischbacher and G. Stolz),
Annales Henri Poincaré 21 (2020), 2327-2366. arXiv| Journal
A class of two-dimensional AKLT models with a gap (with M. Lemm, A. Lucia, B. Nachtergaele, and A. Young),
Contemporary Mathematics, 741, 1-21 (2020). arXiv | Link.
On the regime of localized excitations for disordered oscillator systems (with R. Sims and G. Stolz),
Letters in Mathematical Physics, 110, 1159-1189 (2020). arXiv | Journal.
Entanglement of a class of non-Gaussian states in disordered harmonic oscillator systems.
Journal of Mathematical Physics 59, 031904 (2018) arXiv | Journal.
Correlations in disordered quantum harmonic oscillator systems: The effects of excitations and quantum quenches (with R. Sims and G. Stolz),
Contemporary Mathematics, 717, 31-47 (2018). arXiv | Link.
Localization Properties of the Disordered XY Spin Chain A review of mathematical results with an eye toward Many-Body Localization (with B. Nachtergaele, R. Sims, and G. Stolz),
Analen der Physik (Berlin) 529, 1600280 (2017) arXiv | Journal.
Dynamical entanglement of disordered quantum XY chains (with B. Nachtergaele, R. Sims, and G. Stolz),
Letters in Mathematical Physics 106(5), 649-674, 2016. arXiv | Journal.
A uniform area law for the entanglement of eigenstates in the disordered XY chain (with G. Stolz),
Journal of Mathematical Physics, 56, 121901, 2015. arXiv | Journal
Fast and numerically stable circle fit (with N. Chernov),
Journal of Mathematical Imaging and Vision , 49 (2), 289-295, June 2014. arXiv | Journal.
An adaptive Monte Carlo integration algorithm with general division approach (with M. Alrefaei),
Mathematics and Computers in Simulation, 79 (1), 49-59 , 2008. Journal.
Two sequential algorithms for selecting one of the best simulated systems (with M. Alrefaei),WSEAS Transactions on Systems. 3: 2517-2522, 2004.