On the Mott formula for thermopower of non-interactions electrons in quantum point contacts

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We calculate the linear response thermopower S of a quantum point contact using the Landauer formula and therefore assume non-interacting electrons. The purpose of the paper, is to compare analytically and numerically the linear thermopower S of non-interacting electrons to the low temperature approximation, S¹=(pi²/3e)k² T d(ln G(mu,T=0))/dmu, and the so-called Mott expression, Sᵐ=(pi²/3e)k² T d(ln G(mu,T))/dmu, where G(mu,T) is the (temperature dependent) conductance. This comparison is important, since the Mott formula is often used to detect deviations from single-particle behavior in the thermopower of a point contact.