06-262 Rafael de la Llave, Enrico Valdinoci
Ground states and critical points for generalized Frenkel-Kontorova models (45K, LaTeX) Sep 15, 06
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. We consider a multidimensional model of Frenkel-Kontorova type but we allow non-nearest neighbor interactions. For every possible frequancy vector, we show that there are quasi-periodic ground states which enjoy further geometric properties. The gound states we produce are either bigger or smaller than the state. They are are at bounded distance from the plane wave with the given frequency. The comparison property above implies that the ground states and the translations are organized into laminations. If these leave a gap, we show that there are critical points inside the gap which also satisfy the comparizon properties. In particular, given any frequency, we show that either there is a continuous parameter of ground states or there is a ground state and another critical point which is not a ground state.

Files: 06-262.tex