Nuclear Collective Dynamics and Chaos

The present status and future problems in both the classical-level theory and full quantum theory of nuclear collective dynamics are discussed by putting special emphasis on their relation to the classical and quantum order-to-chaos transition dynamics, respectively. The nonlinear dynamics between the collective and single-particle excitation modes of motion specific for the finite, self-sustained and self-organizing system as the nucleus is discussed within the time-dependent Hartree-Fock (TDHF) theory, the basic equation of which is shown to be formally equivalent to the Hamilton’s canonical equations of motion in the classical nonlinear dynamical system. An importance to relate the structure of the TDHF symplectic manifold with an inexhaustible rich structure of the classical phase space in the nonlinear system is stressed. A full quantum theory of nuclear collective dynamics is proposed under a dictation of what has been developed in the classical-level TDHF theory. It is shown that the proposed quantum theory enables us to explore exceeding complexity of the Hilbert space. It is discussed that a resonant denominator known as a source of the extraordinary rich structure of the phase space trajectories, also plays a decisive role in generating a rich structure of the quantum Hilbert space.