Nontrivial dynamics of a two-site system: Transient crystals

We analyze theoretically quench dynamics of a two-site system abruptly driven from its equilibrium state focusing on the time dependent spectral density function. In the presence of electron reservoirs this function reveals in time a nontrivial regular pattern of peaks corresponding to the stationary quantum chain structure. Such dynamical system with periodic structure of the spectral density stands for a new transient crystal material. We investigate here the role of the Coulomb repulsion between the sites, nontrivial substrates and different system geometries on the transient crystal pattern which can be measured in the tunneling conductance experiments. We also propose the transient crystal system between unbiased leads as an effective monoparametric pump.