This chapter surveys how chaotic motion influences quantum transport. The authors walk through examples where classical chaos and quantum interference meet. They start with single particles, move to many interacting particles, and then discuss systems that exchange energy with their surroundings. Short descriptions of key laboratory experiments are included, especially experiments with cold atoms in optical lattices.

The chapter explains several concrete models. One is the kicked rotor, a particle periodically jolted in angle and momentum. Classically the rotor shows diffusive growth of energy. Quantum mechanically the growth can stop, a phenomenon called dynamical localization. The authors relate this to Anderson localization, a well-known localization of waves in disordered media. They frame such effects using the Floquet operator, which describes evolution over one driving period, and they emphasize that simple number relations between system parameters (for example whether certain ratios are rational or irrational) can switch the system between localized and extended behavior.

Another set of examples uses particles in periodic, driven lattices. The chapter reviews Bloch oscillations, where a particle in a lattice subject to a constant force oscillates instead of drifting. In the tight-binding approximation the particle occupies localized Wannier states and forms an evenly spaced ladder of energies called Wannier–Stark states. If an additional alternating (AC) drive matches the Bloch frequency, those localized states couple into extended states and the particle can move through the lattice again. The authors also discuss how mixing between classically regular and chaotic regions of phase space shows up in the quantum spectrum as avoided crossings and can speed up transport; this effect is often called chaos-assisted tunneling.