Quasi-ballistic scattering in quantum point contact systems

Two scattering models are investigated in quasi-ballistic quantum point contact systems; a model with a few point scattering centres versus the Anderson model with on-site disorder. An exact, recursive Green's function technique is used to obtain magneto-transport quantities such as the conductance fluctuation amplitude and the correlation function. In the quasi-ballistic regime, the two models are not equivalent. The Anderson model can reproduce the same fluctuation amplitude as the `few-scatterer' model, but fails to reproduce the correlation field. When the number of impurities in the `few-scatterer' case is increased towards the diffusive regime, the two models agree well both on the fluctuation amplitude and correlation field. Further, we find that the correlation field in the Anderson model depends dramatically on disorder strength, when moving from the ballistic to the diffusive regime. The importance of the impurity positions in the `few-scatterer' model is also investigated.