Quantum dynamics of charge transfer on the one-dimensional lattice: Wave packet spreading and recurrence

The wave function temporal evolution on the one-dimensional (1D) lattice is considered in the tight-binding approximation. The lattice consists of N equal sites and one impurity site (donor). The donor differs from other lattice sites by the on-site electron energy E and the intersite coupling C. The moving wave packet is formed from the wave function initially localized on the donor. The exact solution for the wave packet velocity and the shape is derived at different values E and C. The velocity has the maximal possible group velocity v = 2. The wave packet width grows with time similar to t(1/3) and its amplitude decreases similar to t(-1/3). The wave packet reflects multiply from the lattice ends. Analytical expressions for the wave packet front propagation and recurrence are in good agreement with numeric simulations.