The role of periodic orbits in coupled, open, ballistic quantum dots

We have performed numerical simulations of the quantum mechanical transport and corresponding wave functions of coupled open quantum dots, with contacts supporting a number of propagating modes. In cases where two dots are connected together in series, we have found that, as has been seen previously in single dots, the wave functions in each dot can be scarred by underlying classical periodic orbits. However, we find that the coupling between dots also allows for a new possibility, whereby resonant wave functions have scars that appear to extend between dots, providing a new variation on the idea that coupled quantum dots can act as artificial molecules. We also consider finite chains of quantum dots, and find behavior analogous to that previously noted for one dimensional superlattices and corrugated structures coexisting with these scarring effects.