What Means Quantum Chaos?
by
Helmut Kroger
Dpartement de Physique, Universite Laval Quebec, Quebec, G1K 7P4, Canada

We will present the following examples of quantum chaos:

(i) An analysis of the level density distribution of the energies of a model in quantum field theory: the scalar \phi⁴ model on a space-time lattice. A set of about 60 energy levels has been computed using the recently develped Monte Carlo Hamoiltonian.

(ii) As an example of use of the quantum action I present results of quantum chaos for 2-D Hamiltonian systems which are classically chaotic. First we consider the system of coupled anharmonic oscillators. We compare Poincaré sections of the quantum action with those of the classical action. We observe chaotic behavior for both. We compare the phase portrait of the classical system with the quantum system, in particular in the neighborhood of hyperbolic fix points. Also we measure the portion of chaotic phase space versus regular phase space. We find indication that the quantum system is less chaotic than its classical counterpart.

Secondly, we consider the Hamiltonian of the Paul trap, which is quite important for atomic clocks, Bose-Einstein condensation etc. We present Poincaré sections as function of temperature and in particular study the chaotic behavior at a transition point from chaos to regular behavior.

Date received: October 18, 2002