Effect of a magnetic flux line on the quantum beats in the Henon-Heiles level density

Abstract

The quantum density of states of the Henon-Heiles potential displays a pronounced beating pattern. This has been explained by the interference of three isolated classical periodic orbits with nearby actions and periods. A singular magnetic flux line, passing through the origin, drastically alters the beats even though the classical Lagrangian equations of motion remain unchanged. Some of the changes can be easily understood in terms of the Aharonov-Bohm effect. However, we find that the standard periodic orbit theory does not reproduce the diffraction-like quantum effects on those classical orbits which intersect the singular flux line, and argue that corrections of relative order variant Planck's over 2pi are necessary to describe these effects. We also discuss the changes in the distribution of nearest-neighbor spacings in the eigenvalue spectrum, brought about by the flux line. (c) 1995 American Institute of Physics.