  Progress in manufacturing technology has allowed us to probe the behavior of
devices on a smaller and faster scale than ever before. With increasing
miniaturization, quantum effects come to dominate the transport properties of
these devices, between collisions, carriers undergo ballistic motion under the
influence of local electric and magnetic fields. The often surprising
propertiesof quantum ballistic transport are currently elucidated in clean
atomic physics experiments. From a theoretical viewpoint, theelectron dynamics
is governed by ballistic propagators and Green functions, intriguing quantities
at the crossroads of classical and quantum mechanics. Here, we briefly describe
the propagator method, some ballistic Green functions, and their application in
a diverse range of problems in atomic and solid state physics, such as
photodetachment, atom lasers, scanning tunneling microscopy, and the quantum
Hall effect.
