How does the connectedness of a quantum graph affect the localization of eigenfunctions?

Math Physics Seminar
Friday, January 26, 2018 - 15:00
1 hour (actually 50 minutes)
Skiles 202
Georgia Tech
Quantum theory includes many well-developed bounds for wave-functions, which can cast light on where they can be localized and where they are largely excluded by the tunneling effect.  These include semiclassical estimates, especially the technique of Agmon, the use of "landscape functions," and some bounds from the theory of ordinary differential equations.  With A. Maltsev of Queen Mary University I have been studying how these estimates of wave functions can be adapted to quantum graphs, which are by definition networks of one-dimensional Schrödinger equations joined at vertices.