Quantum dynamics of a nonlinear kicked oscillator

Abstract

The quantum dynamics of a nonlinear kicked oscillator is studied by a recently proposed complex non-hermitian Hamiltonian technique. It is shown that the probability density and the energy function display either a growing or a decaying exponential time dependence characteristic of absorption or dissipation. It is furthermore shown that though a decrease in the kicking period increases the diffusive motion leading to the ballistic spreading, increasing its value does not apparently favour any localization. The anharmonicity also enhances the dissipative dynamics but with time gives rise to energy crossings typical of a quantum chaos. The variation in the spatial periodicity of the delta-function kicking however exhibits a more complex behaviour showing diffusive character to super-diffusion leading to ballistic motion on the one side and the quantum localization on the other. © 2011 InforMath Publishing Group.