Quantum localization in momentum-space for two coupled kicked rotors

A system of two periodically kicked coupled rotors is studied, to resolve an apparent contradiction regarding localization of states between previously published results, where different models and criteria were used. The system is mapped to an Anderson two-dimensional lattice. The quantum model is evolved numerically for a range of kicking parameters. To check for localization in momentum, the shape of the distribution and the state widths temporal growth are examined for each parameter set. Corresponding classical simulations are also performed as reference, to determine how their distribution widths grow with time, and whether they fall in regular or chaotic regions of classical phase space. The results demonstrate localized and apparently non-localized regimes. However the latter are shown to be consistent with the scaling theory of localization, which gives estimates for their localization lengths and times that far exceed the state size and time span of the simulations performed.