Partial Dynamical Symmetry and Mixed Dynamics

A. Leviatan 1, 2, N. D. Whelan 2, 3

Physical Review Letters 77 (1996) 5202-5205

Partial dynamical symmetry describes a situation in which some eigenstates have a symmetry which the quantum Hamiltonian does not share. This property is shown to have a classical analogue in which some tori in phase space are associated with a symmetry which the classical Hamiltonian does not share. A local analysis in the vicinity of these special tori reveals a neighbourhood of phase space foliated by tori. This clarifies the suppression of classical chaos associated with partial dynamical symmetry. The results are used to divide the states of a mixed system into ``chaotic\'\' and ``regular\'\' classes.

  • 1. Racah Institute of Physics,
    Hebrew University of Jerusalem
  • 2. Division de Physique Théorique, IPN,
    Université Paris XI - Paris Sud
  • 3. Niels Bohr Institute (NBI),
    Niels Bohr Institute