My research has centered on the mathematical study of quantum mechanics and statistical physics, but in recent years I have also worked with entomologists on the application of probabilistic models to problems in field biology. My current research program is funded by the NSF award:

Ergodic Quantum Processes: Localization, Diffusion, and Steady States (2153946)

Prior awards include 1) Localization and Diffusion in Open and Many Body Quantum Systems (1900015 ), 2) Quantum Diffusion in Fluctuating Media (1500386), and 3) Interpreting Data from Trapping of Stochastic Movers (1411411) . Although these projects are distinct in many ways, from the standpoint of mathematical and theoretical physics, they share a common basic feature: both are inspired by the basic scientific question: “What are the effects of disorder?” This question is relevant to any scientific field, since disorder, dirt and noise are all around us!

Selected publications may be downloaded below, and also on the reprints page of this website. A summary of some undergraduate research on trapping of random walkers can be found here.

Selected recent publications related to my current research

• R. Movassagh, J. Schenker, “An ergodic theorem for homogeneously distributed quantum channels with applications to matrix product states,” arxiv:1909.11769

• R. Matos, J. Schenker, “Localization and IDS Regularity in the Disordered Hubbard Model within Hartree-Fock Theory,” arXiv:1906.10800

• R. Mavi, J. Schenker, “Localization in the Disordered Holstein model,” Comm. Math. Phys 364, 719-764 (2018). arXiv:1709.06621.

• R. Mavi, J. Schenker, “Resonant Tunneling In A System With Correlated Pure Point Spectrum,” J. Math. Phys. 60, 052103 (2019). arxiv:1705.03039.

• J. Schenker, “Diffusion in the Mean for an Ergodic Schrödinger Equation Perturbed by a Fluctuating Potential,” Comm. Math. Phys. 339, 859-901 (2015). arXiv:1406.4932

Selected Prior Publications

• J. R. Miller, C.G. Adams, P.A. Weston, J. H. Schenker, Trapping of small animals moving randomly: Principles and Applications to Pest Monitoring and Management. SpringerBriefs in Ecology 2015. 116 pages.

• J. Schenker, “Eigenvector localization for random band matrices with power law bandwidth,” Comm. Math. Phys. 290 (2009), 1065-1097. arXiv:0809.4405

• F. Germinet, A. Klein and J. H. Schenker. Dynamical Delocalization in random Landau Hamiltonians. Ann. of Math., 166 (2007), 215-244.

• M. Aizenman, A. Elgart, S. Naboko, J. H. Schenker, and G. Stolz. Moment analysis of localization in random Schroedinger operators, Invent. Math. 163 (2006), 343-413.

• A. Elgart, J. H. Schenker and G.-M. Graf. Equality of the bulk and edge Hall conductances in a mobility gap. Comm. Math. Phys. 259 (2005), 185-201.

  • Erratum (Comm. Math. Phys. 261 (2006), 545).

• M. Aizenman, J. H. Schenker, R. M. Friedrich, and D. Hundertmark. Finite-volume fractional-moment criteria for Anderson localization. Comm. Math. Phys., 224 (2001), 219–253.

¹Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.