High-frequency blockade in a tight-binding one-dimensional lattice with single vibrating atomic state

One-dimensional tight-binding lattice, single site of which possesses harmonically vibrating level is studied. The states of non-interacting electrons incident with fixed energy from infinity are considered. It is shown that at definite conditions the site reflects electrons {\it absolutely and elastically} (high-frequency blockade states). The problem is treated both numerically and (in the case of narrow band) analytically. The results are compared with the free-electron 1D problem with vibrating $\delta$-functional potential. Together with the blockade states the local and reflectionless states are examined. Possible realization of the system as a lattice of quantum dots is discussed.