Polaron solutions and normal-mode analysis in the semiclassical Holstein model

We investigate polaron properties in the semiclassical Holstein model in one, two, and three dimensions, using two methods: a simple and efficient numerical scheme and a variational approach. We obtain accurate information on the energy and the existence regimes of the polaron state. We study small oscillations of the polaron through normal-mode analysis, investigate their stability, and evaluate the density of states of the polaron eigenfrequencies for different system parameters. The normal-mode analysis shows in the one-dimensional case a pinning-breathing mode crossing in the transition region of the small to large polaron. Similar crossings do not exist in higher dimensions.