Transition from chaotic to regular quantum scattering in mesoscopic billiards with nominally regular geometry

We discuss the origin of a striking transition in the weak localisation lineshape observed in the low temperature magneto-resistance of ballistic quantum dots with square geometry. As the dot openings are gradually closed, the lineshape evolves from a Lorentzian to a linear form and, within the framework of the present theory, this behaviour can only be explained in terms of a corresponding transition from chaotic to regular behaviour within the devices. In order to determine the origin of this transition, we have performed classical simulations of ballistic transport within such dots, taking in to account the nature of the self-consistent potential. Poincare sections for the motion then indeed reveal a transition from chaotic to regular behaviour as the leads are pinched off, which appears to be associated with increasing collimation of the incoming electron beam.