Modular recursive Green’s function method for ballistic quantum transport

A modification of the standard recursive Green’s function method for quantum transport through microstructures is presented which is based on the decomposition into separable substructures. The Green’s functions for these modules are joined by discretized Dyson equations. Nonseparable structures can thereby be calculated with the help of a few recursions with high accuracy. We apply this method to the calculation of ballistic quantum transport through a circular and stadium-shaped quantum dot for high mode numbers to test semiclassical predictions in detail. Among other results we find the breakdown of the semiclassical approximation for long path lengths which is due to the spreading of wave packets in the cavity.