Anderson localization as a parametric instability of the linear kicked oscillator

We rigorously analyze the correspondence between the one-dimensional standard Anderson model and a related classical system, the ''kicked oscillator'' with noisy frequency. We show that the Anderson localization corresponds to a parametric instability of the oscillator, the localization length being related to the rate of exponential growth of the energy of the oscillator. Analytical expression for a weak disorder is obtained, which is valid both inside the energy band and at the band edge.