Chaos in a Hamiltonian description of interacting quantum spins

Regular and irregular dynamics of interacting spins are investigated using the Hamiltonian dynamical system, which completely captures the quantum dynamics. The phase-space and the Hamiltonian dynamics of the quantum system are obtained using the continuous representations and the generalised coherent states of the relevant dynamical group SU(2)×SU(2). The considered model is linear in the generators of the dynamical group, so that the Hamiltonian description is exact. The relation between symmetry of the quantum model and stability of the classical counterpart is studied.