Research
My main research lies in the area of Mathematical Physics, with an emphasis on studying dynamical properties of many-body quantum system:
A particular interest is to prove theorems that help in better understanding of problems that combine effects of disorder and interactions for large quantum systems.
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.
I use a wide range of mathematics, including operator theory, matrix analysis, probability, spectral theory, and operator algebra.
Publications/ Preprints
Entanglement bounds for single-excitation energy eigenstates of quantum oscillator systems (with R. Sims and G. Stolz), Preprint- ArXiv
Slow propagation velocities in Schrödinger operators with large periodic potential (with M. Darras, C. Fischbacher, and G. Stolz), Preprint- ArXiv
Exponentially decaying velocity bounds of quantum walks in periodic fields (with G. Stolz),
Communications in Mathematical Physics 403(2023), 1297-1327. ArXiv| JournalDynamical Evolution of Entanglement in Disordered Oscillator Systems
Reviews in Mathematical Physics 35 (2023) 2350003 (32 pages) . ArXiv| JournalEntanglement bounds in the XXZ quantum spin chain (with C. Fischbacher and G. Stolz),
Annales Henri Poincaré 21 (2020), 2327-2366. ArXiv| JournalA 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),
Ann. der Phys. (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 | JournalFast 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. pdf.