  Using suitable magnetic flux operators established in terms of discrete
derivatives leads to quantum-mechanical descriptions of LC-circuits with an
external time dependent periodic voltage. This leads to second order discrete
Schrodinger equations provided by discretization conditions of the electric
charge. Neglecting the capacitance leads to a simplified description of the
L-ring circuit threaded by a related time dependent magnetic flux. The
equivalence with electrons moving on one dimensional (1D) lattices under the
influence of time dependent electric fields can then be readily established.
This opens the way to derive dynamic localization conditions serving to
applications in several areas, like the time dependent electron transport in
quantum wires or the generation of higher harmonics by 1D conductors. Such
conditions, which can be viewed as an exact generalization of the ones derived
before by Dunlap and Kenkre [Phys. Rev. B 34, 3625(1986)], proceed in terms of
zero values of time averages of related persistent currents over one period.
