Hidehiko Tsukuma

Bifurcation structure of eigenstates and periodic trajectories in TDHF phase space —Interference effects in eigenstates

The resonant periodic trajectories in time-dependent Hartree-Fock phase space are found to be bifurcated from simple vibrational trajectories in a three-level model Hamiltonian. Corresponding to the bifurcated periodic trajectories, there are series of resonant eigenstates with characteristic profile function shapes. In terms of resonant basis system, it is pointed out that the quantum mechanical resonance overlap mechanism determines the stability of the eigenstates.

BIFURCATION STRUCTURE OF EIGENSTATES AND PERIODIC TRAJECTORIES IN TDHF PHASE SPACE : WEAK NONLINEARITY CASE IN SU(3) MODEL

To find out how quantum bifurcation phenomena manifest themselves in the space of states, various periodic trajectories accompanied with several sets of bifurcated trajectories are studied for a simple quantum model Hamiltonian under a time-dependent mean-field approximation. Making use of the quantum-classical correspondence, a method of classifying the eigenstates and of visualizing the global structures of the whole space of eigenstates is proposed. By means of the profile functions of the eigenstates, appropriate sets of eigenstates representing the quantum correspondents of the bifurcations are found. The idea of quantum bifurcations is supported by similar behavior of the energy vs period time (E-T) plots of the periodic trajectories and the eigenstates.