Wave function scarring effects in open ballistic quantum cavities

Numerical simulations have been carried out of the magneto-transport and corresponding wave functions of two quantum dot structures, namely the stadium and the Sinai billiard. In our simulations, the Schrödinger equation is mapped onto a tight-binding lattice by replacing derivatives by finite differences, and the conductance is calculated via the Landauer formula following the application of an iterative technique to translate across the structure. In both structures, many of the resonance features in the transport show scarring, that is, the amplitude of the corresponding wave functions is highly concentrated along underlying periodic classical orbits. Our analysis indicates that certain periodicities evident in the magneto-transport can be associated with particular orbits.