Quantum Kicked Rotor in a Highly Inhomogeneous Magnetic Field

Abstract

A new model of a spin-1/2 quantum kicked rotor coupled with a highly inhomogeneous magnetic field is proposed. The model is mapped into the appropriate tight-binding equations, and then the problem of localization is considered. The introduced tight-binding model is verified by calculating the localization length for the appropriate quasi-energy states. In particular, it is shown that the functional form of the spin-dependent term in kicking potential is exclusively responsible for the growth of the localization length with an increase in the magnitude of the magnetic field. The growth is more pronounced if the inhomogeneity of the magnetic field is greater. Thus, quasi-extended states appear as a consequence of strongly conspicuous inhomogeneity, and they exhibit nonstandard localization properties. Their existence is also shown by calculating the appropriate inverse participation ratio and pair-correlations. Therefore, some kind of "localization–delocalization" transition is possible here. This has been demonstrated as well by following the time evolution of the wave packet in the angular momentum space, assuming increasing inhomogeneity. For extremely large inhomogeneity, dynamical localization is destroyed. The model proposed here can serve as an assessment simulator for the induced electric dipole moment in a hydrogen-like atom, assuming the existence of anisotropy.