Wave Function Scarring Effects in Open Ballistic Quantum Cavities

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