N masses on a string
Paul Martin, Professor
Date and time:
Friday, October 18, 2013 - 3:00pm
Solving the one-dimensional wave equation is an undergraduate problem. We consider problems of time-harmonic waves interacting with N scatterers: they could be beads on a long string, for example. If the scatterers are identical and equally spaced, we obtain a problem that can be solved exactly. This is true when N is finite or infinite. Our main interest is with disordered problems, where a periodic configuration is disturbed. For example, we could change just one scatterer in a finite periodic row. It turns out that this problem can be solved exactly. Similar problems where every scatterer in the row is disturbed are also discussed. The main tools used are perturbation theory and transfer matrices. The main motivation comes from a desire to understand the competition between wave propagation in almost-periodic structures and localization phenomena in random media.