This project represents a research program to study the discrete self-trapping (DST) equation. This equation serves as a model for many important effects in applied science ranging from charge transport in crystals to protein dynamics. Basic properties of the classical DST equation are reviewed and a straightforward quantum procedure is outlined. The proposed research includes: i) Study of a phase transition that appears as anharmonicity is increased, ii) Study of DST for many degrees of freedom, iii) Determination of the effects of anharmonicity in DST on "Anderson localization", and iv) Applications of the quantum theory to compute power spectra of solution trajectories.
