A brief comparison between two programs that compute the static conductance of a disordered two-dimensional tight-binding system

There are two programs in the CPC program library that compute the static c onductance of a disordered two-dimensional cluster described by a tight-bin ding Hamiltonian. The older program uses the Landauer scheme to get the con ductance from the transmittance of a cluster attached to two semi-infinite chains that play the role of physical leads. The second program directly us es the Kubo formula to get the conductance of a similar cluster connected t o leads of arbitrary width. Tn both cases, the local Green function should be calculated, but while the first method uses the idea of recursion and im plements a set of subroutines to get the desired matrix elements of the res olvent, the second method employs LAPACK subroutines to propagate the self- energy matrix from one side of the cluster to the other. At the end both me thods deliver the same numerical answer, with a comparable high precision b ut at quite different computing speeds. The newer method is typically one o rder of magnitude quicker thanks to modem methods in Linear algebra when ju st one system is solved, but recursion is advantageous for solving the same systems for several Fermi energies because in this case the slow part of t he calculation is done only once. (C) 2000 Elsevier Science B.V. All rights reserved.