In case of incoherent transport, the electron wave-functions can not be
described by a single phase over the entire sample. If one considers
multiple reflections, for example between scattering centers and , the overall
between these two scattering centers is given by
where the effect of interference during a scattering event is neglected.
One can rewrite (2.26) as
Using the formula for the resistance given by (2.25)
and (2.27), one can see that the resistance of the wire is
. Applying this result to the case of
is an average
transmission probability for an individual scattering event over a mean free
path. Thus the total resistance is given by a series connection of microscopic
resistances. This is nothing but OHM's law, according to which the microscopic
resistance is proportional to .
M. Pourfath: Numerical Study of Quantum Transport in Carbon Nanotube-Based Transistors