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The Landauer formula for a one dimensional quantum system (potential step scattering) can be written as

$$ I(V)=\frac{2e}{h}\int_{-\infty}^\infty dE T(E) (f_S(E) - f_D(E)), $$

where $T(E)$ is the transmission probability and $f_i(E)$ is the Fermi function of source $S$ or drain $D$. In Cuevas it is claimed that if the temperature is zero (Fermi functions are potential steps) and if low voltages is assumed, the expression reduces to

$$ I = GV, $$

where the conductance is given by $G=(2e^2/h)T$.

What is the low voltages assumption? In other words, if I assume low voltages, along with zero temperature, what is left to compute in the integral?

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In general, the relationship $I(V)$ for arbitrary voltages is nonlinear in the voltage difference $V$, and the assumption of low voltage allows one to write the linear approximation $I \approx GV$ by expanding at first order the difference of the Fermi-Dirac functions.

At zero temperature, the relationship $I(V)$ is still nonlinear unless $T(E)$ is a constant independent of $E$.

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