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\sect{Landauer formula for a 1D conductance}

Consider 1D conductor that has transmission coefficient $g$.
The conductor is connected to 1D leads that have
chemical potentials $\mu_a$ and $\mu_b$.
Assume ${\mu_a=\mu}$ and ${\mu_b=\mu+eV}$, where $V$ is the bias.

\Dn

(1) Write the expression for the current $I$ as an integral
over the occupation function $f(\epsilon)$.

\Dn

(2) For small bias write the relation as $I=GV$
and obtain an expression for $G$.
Write explicit results for zero temperature Fermi occupation
(Landauer formula)
and for high temperature Boltzman occupation.

\Dn

(3) Find expressions for $I(V)$ in the case of
arbitrary (possibly large) bias,
for zero temperature Fermi occupation
and for high temperature Boltzmann occupation.
Assume that $g$ is independent of energy.


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