An the spectrum for the time evolution of a periodically rank-N kicked Hamiltonian

Full text: We find the conditions under which the spectrum of the unitary time evolution operator for a periodically rank-N kicked system remains pure point, generalising the work of Combescure and providing a unitary equivalent to the self-adjoint work by Howland. Relaxing this condition, we characterise the emergence of a continuous spectrum (as in) and comment on the importance of such a continuous spectrum in the field of quantum chaos. A number of generally held misconceptions in the physics literature will be highlighted, including mistakes made. Much of this work is presented in detail. Copyright (2005) Australian Institute of Physics