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Differential Equations Seminar: The geometry of quantum diffusion

Felipe Hernandez (Stanford)
Thursday, January 19, 2023
4:00-5:00 PM
The phenomenon of wave propagation in random environments appears in many physical situations of practical interest. The simplest model for this phenomenon is the Schrodinger equation coupled to a weak random potential, which describes the evolution of an electron in disordered media. The effect of the disorder is to scatter the wave into random directions. The long-time behavior is described by an effective diffusion equation, which was first established by Erdös, Salmhofer, and Yau using sophisticated diagrammatic arguments. In this talk I will describe a new approach to proving this effective limit which uses a wavepacket decomposition of the solution to give a geometric meaning to the diagrams. I will focus on the geometry of the diagrams and state some elementary open problems concerning Euclidean geometry which suggest a path to simpler proofs and stronger results.
Building: Off Campus Location
Location: Virtual
Event Link:
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics, Differential Equations Seminar - Department of Mathematics