Parametric variation of resonances for regular and chaotic scattering

We study the trajectories of resonances in the complex energy plane as a function of a control parameter for simple systems whose classical counterparts are regular and chaotic. We analyze the influence of the classical phase space structure on the parametric variations of resonances. We employ both the Pechukas-type equations of motion as well as periodic orbit quantization. Examples considered include hydrogen in a strong electric field, the hydrogen atom in a strong magnetic field, and doubly excited resonances in the isoelectronic sequence of helium.