Chaotic scattering, unstable periodic orbits, and fluctuations in quantum transport.

The field of quantum chaos has recently focused attention on the quantum description of chaotic scattering processes. The new physical intuition, analytical methods, and numerical tools developed in the study of the quantum behavior of classically chaotic bound systems, like quantum billiards or atoms in strong fields, has led to exciting new predictions for the scattering of electromagnetic waves in curved waveguides, electrons in mesoscopic wires, and atoms off molecules. After a brief review of recent progress in the field of quantum chaos, this paper focuses on specific results relating to ballistic electron transport in small, mesoscopic devices. Several specific geometries are suggested for experimental studies of this "game" of quantum pinball with explicit predictions for the fluctuations in the electrical conductivity as functions of the electron Fermi energy and of an applied magnetic field.