Breking of Separability Condition for Dynamical Collective Subspace: Onset of Quantum Chaos in Large-Amplitude Collective Motion
Fumihiko Sakata, Y. Yamamoto, Toshio Marumori +2 more
It is the purpose of the present paper to study “global structure” of the state space of an N-body interacting fermion system, which exhibits regular, trasientand stochastic phasesdepending on strength of the interaction. An optimum representation called a dynamical representationplays an essential role in this investigation. The concept of the dynamical representation has been introduced in the quantum theory of dynamical subspacein our previous paper, in order to determine self-consitently an optimum cokkective subspace as well as an optimum collective Hamiltoninan. In the theory, furthermore, dynamical conditions called separabilityand stability conditionshas been provided in order to identify the optimum collective subspace as an approximate invariant subspaceof the Hamiltonian. Physical meaning of these conditions are clarified from a viewpoint to relate breakingof them with bifurcationof the collectivity and an onset of quantum chaosfrom the regularcollective motion, by illustrating the general idea with numerical results obtained for a simple soluble model. It turns out that the onset of the stochastic phase is associated with dissolution of the quantum numbers to specify the collective subspace and this dissolution is induced by the breaking of the separability condition in the dynamical representation.
Progress of Theoretical Physics•Nov 1, 1989•6 citations