New Mathematical Tools for Quantum Technology

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.