Absence of quasiperiodicity in a kicked quantum rotator and a new localization-delocalization transition

Abstract

It is found that the angular momentum fluctuations of a solvable kicked quantum rotator become unbounded in time if the kicking potential is discontinuous. This differs from the quasiperiodic behavior found for regular potentials and offers a possible route to quantum chaos. With use of a recently found mapping of the kicked rotator to an Anderson problem of conduction in a one-dimensional disordered lattice, our result implies a new localization-delocalization transition if the hopping matrix element decays more slowly than ${n}^{\ensuremath{-}1}$, where $n$ is the number of lattice sites connected by it.