With the rise of the use of fiber optics in our society, a demand has arisen to understand more about the properties of wave guides, which is the technical term for the type of conducting medium in fiber optic cables.

In the conductance of electric current through wave guides, the electrons which carry the current can be modeled as classical particles,but they can also be modeled as quantum wave functions.

If the electron is modeled as a classical particle, the motion of the electron may be chaotic, depending on the geometry of the wave guide itself. As part of their on-going research into quantum chaos, Prof. Linda Reichl and Kyungsun Na have recently shown that in the quantum model, the conductance of the wave guide displays different features depending on whether or not the underlying classical system is integrable or non-integrable.

The diagram at left, for example, is a numerical prediction of the probability amplitude of an electron in a "rippled chanel." The unevenness of the wave function is typical in the case where the classical Poincaré surface-of-section is chaotic. These numerical results may lead to a better understanding of the geometric properties of all types of conducting media.