Kinetic Analysis of the Migration of Vibrational Excitations in Harmonic and Anharmonic Dendrimer Model Systems

The migration of vibrational excitations in a dendrimer is analyzed, based on the kinetic equations for harmonic and anharmonic model systems consisting of identical oscillators coupled with each other. We estimate the probability that two one-quantum excitations migrate and unite into a two-quantum excitation at the central oscillator for model systems with different branching generations. When oscillators are all purely harmonic, the probability decreases drastically with the size of the dendrimer. With the introduction of anharmonicity, we show that the concentration process of one-quantum excitations at neighboring two oscillators to a two-quantum excitation at one of the pair becomes more advantageous than the inverse process. We then conclude that the anharmonicity in the oscillators effects suppression of the decrease of the probability as seen in the harmonic oscillator model.