Quantum mechanics and diffusion on metric graphs

Math Physics Seminar
Thursday, December 1, 2022 - 4:00pm for 1 hour (actually 50 minutes)
Skiles Room 005
Evans Harrell – School of Mathematics, Georgia Tech – harrell@math.gatech.edu
Michael Loss

Quantum mechanics and diffusion on a network, in the sense of a metric graph, are locally one-dimensional, but the way the graph is connected can add multidimensional features and some strange phenomena.  Quantum graphs have been an active area of research since the 1990s.  I’ll review the subject and share some ideas about analyzing Schrödinger and heat equations on metric graphs, through the associated eigenvalue problem and the heat kernel.

This talk is based on a 2022 article with David Borthwick and Kenny Jones, and on work in progress with David Borthwick, Anna Maltsev, and Haozhe Yu.