The relation ξ=(1/2D${ħ}^{\mathrm{-}2}$ between the localization length ξ and the diffusion coefficient D of the kicked rotor is derived in the framework of the scaling theory for localization. It is argued that this relation, first found by Shepelyansky [Phys. Rev. Lett. 56, 677 (1986); Physica 28D, 103 (1987)], reveals the special importance of the Lloyd model for the understanding of the quantal behavior of the kicked rotor and other dynamical systems. The finite-size-scaling form of the localization length and the conductance of the Lloyd model are derived.

• Received 20 June 1988

DOI:https://doi.org/10.1103/PhysRevA.39.1628