Quantum transport in single and multiple quantum dots

Ballistic quantum dots have been used in a wide variety of studies ranging from single-electron charging to chaotic systems. However, in open, ballistic quantum dots, the behavior is significantly different. Here, we discuss (1) the observation of regular, periodic fluctuations arising from the existence of stable orbits, (2) the regular and chaotic behavior of coupled dots, and (3) the theory of such dots. The regular orbit properties of these dots are their most stable, generic property, and are clearly reflected in the magnetoresistance. These give rise to periodic fluctuations, which are the result of a very few, periodic orbits within the dot that give rise to scarred wave functions and harmonically related frequencies in the Fourier spectrum. The orbits arise from the role of regular trajectories in the oscillatory density of states and the crucial collimation effects of the quantum point contacts.