My research program combines fundamental advances in mathematical physics with practical applications relevant to emerging technologies. This work contributes to both theoretical understanding and technological innovation. More technically, I focus on Schrödinger operators, using scattering and spectral theory tools; I am also interested in periodic systems and, more specifically, twisted bilayer graphene. My recent projects revolve around twisted bilayer graphene and ballistic transport, as well as systems that are partially periodic.
I have recently completed a project offering a new approach to analyzing twisted bilayer graphene from first principles without relying on the famous Bistritzer-MacDonald model and its approximations. This work aims to lay the groundwork that will allow, later on, a more direct approach to the magic angles observed in these systems. In this work, I analyzed this system for commensurate angles- angles that still have periodic structure- and showed the existence of Dirac cones in the vertices of the Brillouin zone, and showed that the slope of the Dirac cones is small for commensurate angles that are close to incommensurate angles. I created a simulation of this in Python- see here.
📊 ACADEMIC IMPACT: Advancing fundamental understanding of electronic band structures in moiré materials, contributing to spectral theory and periodic operator analysis.
🏭 TECHNOLOGY RELEVANCE: This research informs the development of novel electronic devices and quantum materials for next-generation computing applications.
Before that, I had a collaboration studying ballistic transport in systems with a potential that is periodic in some directions and compactly supported in others. We managed to show that a subset of the surface states in such a system exhibits directional ballistic transport, as well as that a dense subset of all scattering states exhibits ballistic transport in all directions.
My thesis revolves around systems where the potential decays only in some, but not all, directions. In collaboration with Adam Black, this work generalizes the usual setting of short-range scattering to various general geometries. By utilizing microlocal tools, we showed that for such operators, any function decomposes into two components that differ by their asymptotic behavior in time.
📊 THEORETICAL CONTRIBUTIONS: Extending scattering theory to new geometric settings using microlocal analysis and PDE techniques.
🏭 PRACTICAL APPLICATIONS: Understanding electron transport is crucial for designing quantum devices and optimizing electronic material properties.
Before starting my graduate program, I worked for the Israeli Atomic Energy Commission as a researcher and later as head of the nuclear reactor physics group. My research required intimate knowledge of our reactor and a deep understanding of its physics. One of the projects I worked on, which later became my M.Sc. thesis, was to generalize the current noise experiments formalism to include energy and spatial dependencies.
In addition to my current research, I am also involved in an ongoing project with a doctor from Yale Medical School to develop a general mathematical framework for analyzing steady-state experiments for determining metabolic rates.