Dynamical impurity in a tight-binding Hamiltonian model

We find the exact dynamics-in mean value-for a one-dimensional tight-binding model in the presence of a dynamical impurity (dichotomic process). Using the theorem of Bourret et al we prove that a 'dynamical localization' of the TB wave function electron is indeed generated by the stochastic impurity. Our results can also be interpreted in terms of a 'quasi-particle', representing the excitation of the system interacting with its surroundings. A lifetime and an energy can be associated with this quasi-particle. This lifetime appears as an irreversible process occurring due to the interaction with the stochastic impurity.