Classical and quantum formalism of mode-based atomic-scale descriptions of lattice distortions

We present classical and quantum mechanical atomic scale theory of lattice distortions using atomic scale modes and their constraint equations. The formalism is demonstrated for a 1-dimensional chain and a 2-dimensional square lattice. We comment on the application of the mode-based atomic-scale approach for systems with strong anharmonicity and structural phase transitions. \newline \newline [1] K. H. Ahn, T. Lookman, A. Saxena, and A. R. Bishop, Phys. Rev. B 68, 092101 (2003); \newline [2] K. H. Ahn, T. Lookman, and A. R. Bishop, Nature 428, 401 (2004).