"Ping-pong" electron transfer. I. First reflection of the Loschmidt echo

Quantum dynamics of the electron wave function on one-dimensional lattice is considered. The lattice consists of $N$ equal sites and one impurity site. The impurity site differs from other sites by the on-site electron energy $E$ and the hopping integral $C$. The wave function is located on the impurity site at $t = 0$. The wave packet is formed which travels along the lattice, and reflects from its end. Reflections happen many times (Loschmidt echo) and this phenomenon is considered in the second part of the paper. Analytical expressions for the wave packet front propagation at different values $E$ and $C$ are derived, and they are in excellent agreement with the numerical simulation. The obtained results can help in interpretation of recent experiments on highly efficient charge transport in synthetic olygonucleotides.