The calculation of transmission and resonance properties of quantum devices using methods from chemical reactive scattering

Abstract

Two relatively new methods, the spectral projection method and the stabilization method, of implementing scattering calculations are described, and are here applied to two devices. Both methods use essentially short range spectral projection operators to produce a complete set of solutions of the wave equation that need be valid only inside the interaction region. While the spectral projection method is more generic than the stabilization method which is based on using the more difficult to compute spectral density operator, the latter becomes very efficient when narrow resonances exist. For problems of small size both methods are practical in the sense that they involve only real, symmetric matrices resulting from Hamiltonians represented on L 2basis sets. For more challenging larger systems the spectral projection method lends itself to a very efficient time independent iterative procedure that obtains results simultaneously at all energies. This procedure uses modified Chebyshev recursion relations to essentially expand the operator ( E− H) −1. It requires minimal storage and the resulting series converges rapidly in a manner that is uniform in energy.