Critical Phenomena of Dynamical Delocalization in Quantum Anderson Map

Using a quantum map version of one-dimensional Anderson model, the localization-delocalization transition of quantum diffusion induced by coherent dynamical perturbation is investigated in comparison with quantum standard map. Existence of critical phenomena, which depends on the number of frequency component $M$, is demonstrated. Diffusion exponents agree with theoretical prediction for the transition, but the critical exponent of the localization length deviates from it with increase in the $M$. The critical power $ε_c$ of the normalized perturbation at the transition point remarkably decreases as $ε_c \sim (M-1)^{-1}$.

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