Universal Anderson localization in one-dimensional unitary maps

Abstract

We study Anderson localization in discrete-time quantum map dynamics in one dimension with nearest-neighbor hopping strength ? and quasienergies located on the unit circle. We demonstrate that strong disorder in a local phase field yields a uniform spectrum gaplessly occupying the entire unit circle. The resulting eigenstates are exponentially localized. Remarkably this Anderson localization is universal as all eigenstates have one and the same localization length L-loc. We present an exact theory for the calculation of the localization length as a function of the hopping, 1/L-loc = |ln (| sin(?)|) , which is tunable between zero and infinity by variation of the hopping ?.