We investigate a semiclassical dynamics driven by a high-frequency Ω inhomogeneous field, plus a static arbitrary potential on a one-dimensional tight-binding lattice. We find - in the approach of Kapitza's pendulum - an effective, time independent potential that describes the average of the electronic motion to order Ω-2. This effective potential depends on the static external potential, on the lattice constant and on the applied high frequency field. Remarkably, we find that the dynamic correction of rapidly oscillating fields is formally identical to that associated to Kapitza's usual continuum result. Finally, applications are made to: the harmonic oscillator on the lattice, the Bloch oscillation effect and "dynamical localization" in arrays of optical waveguides (wherein an experimental prediction is made).
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