Hopping and correlation effects in atomic clusters and networks

Abstract

Exact solution for hopping and correlation effects in atomic clusters and mesoscopic/nanoscopic networks is outlined. The program translates the Hamiltonian operator of the cluster written in terms of second-quantized creation and annihilation operators, to sparse matrix of (extremely) large dimension and solves the latter with the help of new compiler termed ABC ("Advanced Basic-C" compiler/converter/programmer). The ABC creates a stand-alone executable or, if proved necessary, source C-code received from the original program written in a simplified Quick Basic dialect. ABC employes mathematical functions including the complex variables, arbitrary precision floating-point numbers, special functions, standard mathematical routines (mulidimensional integrals, eigenvalues of Hermitian marices, in particular a new algorithm for sparce Hermitian matrices, etc.) and is appropriate to practically all software/hardware environments (Windows, OS/2, Linux and UNIX machines).