Research Interests

I am interested in mathematical and theoretical physics and biology.  Mathematical physics is a branch of pure mathematics with the aim of deriving rigorous results for equations or models suggested by physical theory. The general goal is to produce mathematical results which illustrate or illuminate the theory; to prove theorems, with consequences for science, based on mathematical structures abstracted from physics.  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. Although these two projects are distinct in many ways, from the stand point 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

• J. Fröhlich, J. Schenker, “Quantum Brownian motion for Lindblad dynamics in the presence of disorder,” J. Math. Phys. 57, 023305 (2016). arXiv:1506.01921  
• Schenker, J., "Diffusion in the Mean for an Ergodic Schrödinger Equation Perturbed by a Fluctuating Potential." Comm. Math. Phys. 339, pp 859-901. arXiv:1406.4932   
• Schenker, J., "How large is large? Estimating the critical disorder for the Anderson model." Lett. Math. Phys. 95, 53-66. arXiv:1305.6987.  
• Schenker, J., "Eigenvector localization for random band matrices with power law band width." Comm. Math. Phys. 290, 1065-1097. arXiv:0809.4405.