Article ID Journal Published Year Pages File Type
1901213 Reports on Mathematical Physics 2006 11 Pages PDF
Abstract

We study approximations of billiard systems by lattice graphs. It is demonstrated that under natural assumptions the graph wave functions approximate solutions of the Schrödinger equation with energy resealed by the billiard dimension. As an example, we analyze a Sinai billiard and a scattering system obtained by attaching a pair of external leads to it. The results illustrate emergence of global structures in large quantum graphs.

Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics