Some analytical results in phase coherent transport in quantum wire

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 method for the calculation of the Greenʹs function (GF) and the coherent transmission coefficient. 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.