Classical and Quantal Chaos Described by a Fourth Order Quadrupole Boson Hamiltonian

Abstract

A quadrupole boson Hamiltonian is considered within a time dependent variational formalism. The trial functions are coherent states with respect to the quadrupole bosons [Formula: see text] and [Formula: see text]. The character, chaotic or regular, of the classical trajectories are studied, in terms of both the Poincaré surface of sections and maximal Lyapunov exponents, as a function of energy and an order parameter B, the coefficient of the third order boson term. A peculiar feature concerning the behavior of chaos and order in the range of large energies is pointed out. Quantizing the classical energy function one obtains an operator whose spectrum is analyzed in terms of level spacing distribution, Some classical and quantal features of the chaotic motion are possibly related.