Surface Energies Arising in Microscopic Modeling of Martensitic Transformations

In this talk I present and analyze a two-well Hamiltonian on a 2D atomic lattice for low energy states. The two wells of the Hamiltonian consist of the SO(2) orbit of two rank-one connected matrices. Seeking to obtain an understanding of the origin of surface energies, I focus on special $(1+\epsilon)-dimensional$ states, certain "atomic chains". For these I explain the formation of the twinning and boundary layers. This is joint work with G. Kitavtsev and S. Luckhaus.