Comment on: ‘‘A quantum analog to the classical quasiperiodic motion’’

Michael Berry

Gabriel Hose, Howard S. Taylor

The comments Mukamel2 on a previous paper by the authors1, regarding the quantum analog to quasiperiodic motion in classical mechanics are answered. The effective Hamiltonian is defined for each state and yields the quasiconstants of the motion for the state of interest. This is not the Heff given by Mukamel2. (AIP)

Michael J. Davis, Eric J. Heller

Tunneling involves an allowed quantum event which fails to take place classically. Dynamical tunneling is the subset of such events which do not involve a classically insurmountable potential barrier. In this paper, we present unambiguous evidence for dynamical tunneling in bound state quantum systems.The tunneling occurs between two distinct regions of classically trapped quasiperiodic motion. Close analogies are shown to exist between this situation and ordinary barrier penetration in a double minimum potential. In the cases we study, tunneling occurs between equivalent or nearly equivalent local mode motions, which have arisen out of a resonance between the symmetric and nonsymmetric stretch.

Jean-Louis Basdevant, Jean Dalibard

Yoshio MURATA

Arthur Hobson

It is shown that the usual proofs of the quasiperiodicity of isolated, finite quantum-statistical systems, previously thought to be general proofs, are in reality based on the special case of a discrete array. Quasiperiodicity is demonstrated for the analogous special case (the discrete distribution) in classical statistical mechanics. The density-operator formalism is set up for the case of a continuous array. The question of the possibly irreversible behavior of isolated, finite quantum-statistical systems with continuous arrays is investigated. An argument is given indicating that such systems generally behave irreversibly. The situations in classical and quantum statistics then appear to be entirely analogous, since it is well known that isolated, finite classical-statistical systems may, in the case of a continuous distribution (the analog of a continuous quantum-statistical array), behave irreversibly.