Response Function of an Irregular Oscillator

Properties of the response functions for a two-dimensional quartic oscillator are studied based on the diagonalization of the Hamiltonian in a large model space. In particular, response functions corresponding to a given momentum transfer are studied for different values of the coupling parameter in the Hamiltonian. The latter controls regular or chaotic nature of the spectra and eigenstates of the system. Fluctuation properties of the energy-strength correlation of the response are investigated. Even when the statistical properties of the system indicate an almost completely chaotic character, there remains a typical structure in the response function similar to that in the regular system. The nature of this structure is studied in some detail.