Quantum transport in linear chains under periodic perturbations

Quantum transport properties across a time dependent impurity in a linear chain are studied theoretically using the Floquet formalism. We obtain the exact reflection coefficient for a wide range of parameters. Our results compare well with known approximations in the high frequency regime. Furthermore, at lower frequencies we observe new features and a significant departure from the approximated predictions. Below a well defined frequency the impurity couples waves of differing $k$-values. As a result, the impurity not only splits the incident wave into a transmitting and a reflecting part of the same wave number $k$, but also waves of differing $k$ emerge from the perturbed site. The amplitude of these waves is also obtained.