Open Problems on Billiards and Geometric Optics

Problems on Billiards

2 Echo spectroscopy and Atom Optics Billiards

We discuss a recently demonstrated type of microwave spectroscopy of trapped ultra-cold atoms known as " echo spectroscopy " [M.F. Andersen et. al., Phys. Rev. Lett., in press (2002)]. Echo spectroscopy can serve as an extremely sensitive experimental tool for investigating quantum dynamics of trapped atoms even when a large number of states are thermally populated. We show numerical results fo...

On plane geometric spanners: A survey and open problems

Given a weighted graph G = (V,E) and a real number t ≥ 1, a t-spanner of G is a spanning subgraph G′ with the property that for every edge xy in G, there exists a path between x and y in G′ whose weight is no more than t times the weight of the edge xy. We review results and present open problems on different variants of the problem of constructing plane geometric t-spanners.

Open Billiards and Ergodic Theory

REFRACTION PROBLEMS IN GEOMETRIC OPTICS April 22, 2013