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We consider periodically driven Anderson insulators. The short time behaviorfor weak, monochromatic, uniform electric fields is given by linear responsetheory and was famously derived by Mott. We go beyond this to consider bothlong times---which is the physics of Floquet late time states---and strongelectric fields. This results in a `phase diagram' in the frequency-fieldstrength plane, in which we identify four distinct regimes. These are: a linearresponse regime dominated by pre-existing Mott resonances, which existsprovided Floquet saturation is not reached within a period; a non-linearperturbative regime, which exhibits multiphoton-absorption in response to thefield; a near-adiabatic regime, which exhibits a primarily reactive responsespread over the entire sample and is insensitive to pre-existing resonances;and finally an enhanced dissipative regime.

Mott, Floquet, and the response of periodically driven Anderson insulators