Energy Transport by Acoustic Modes of Harmonic Lattices
Energy Transport by Acoustic Modes of Harmonic Lattices
We study the large scale evolution of a scalar lattice excitation u which satisfies a discrete wave equation in three dimensions, $\ddot u_t(\gamma)=-\sum_{\gamma'}\alpha(\gamma-\gamma')u_t(\gamma')$, where $\gamma,\gamma'\in\mathbb{Z}^3$ are lattice sites. We assume that the dispersion relation $\omega$ associated to the elastic coupling constants $\alpha(\gamma-\gamma')$ is acoustic; i.e., it has a singularity of …