Quantum Nonlinear Resonance

Abstract

To visualize complex structure of the excited states in the many-fermion system, a profile function of the eigenstate within the quantum phase space is defined by using the boson expansion theory. When the anharmonic interaction is sufficiently weak where a corresponding semi-quantum system described by the time-dependent Hartree-Fock (TDHF) theory shows isolated resonant structure, there exists a remarkable similarity between the Poincaré section map of the TDHF trajectories and the profile functions of the eigenstates. It is shown that these eigenstates are well understood by using a new concept of quantum nonlinear resonance. It is also shown that a pair of newly appeared states due to the quantum resonance is not associated with any dissolution in a number of the good quantum numbers.