Some analytic results in coherent quantum transport
  A quantum wire of uniform cross section (but with eventual disorder) with three regions: dot, left lead, and right lead, is considered. Assuming that the same unitary transformation diagonalizes all unit cells of this wire, we propose a new formula for the calculation of the Greens function (GF) and the coherent transmission coefficient. This formula allows to calculate these quantitites much faster than the standard methods. In particular, the problem of a uniform dot (simple cubic uniform dot attached to the simple cubic wire), with all onsites equal and all hoppings equal is solved fully analytically. The energy and dot-length dependence of the GF, local density of states (LDOS), the transmission coefficient and bound state energies are also derived. 
Mohammad Mardaani, Keivan Esfarjani