Parametric dynamics of resonances in quantum systems

The dependence of resonances (i.e., positions and widths) on a control parameter of the Hamiltonian can be described by a set of coupled ordinary differential equations which could be useful to identify the fingerprints of classical chaos on the quantum mechanics. We investigate the numerical solutions of this set of differential equations. The major advantage of this approach lies in the fact that a single solution provides open-quotes en routeclose quotes the resonances for all parameters in the integration interval. Therefore, each resonance can be easily identified in contrast to other methods when the density of resonances is high and resonances begin to overlap. Using this method, we determine parametric open-quotes trajectoriesclose quotes of resonances for hydrogen in a strong electric field