The Classical Diffusion-Limited Kronig–Penney System

Abstract

We have previously discussed the classical diffusive system of the bounded onedimensional multitrap using the transfer matrix method which is generally applied for studying the energy spectrum of the unbounded quantum Kronig-Penney multibarrier. It was shown, by this method, that for certain values of the relevant parameters the bounded multitrap array have unity transmission and a double-peak phase transitional behavior. We discuss in this work, using the same transfer matrix method, the energy related to the diffusion through the unbounded one-dimensional multitrap and find that it may be expressed in two entirely different ways with different results and consequences. Also, it is shown that, unlike the barriers in the Kronig-Penney case, the energies at one face of the imperfect trap greatly differ from the energies at the other face of the same trap.