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

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, S = (π/3e)k BT∂μ[lnG(μ, T = 0)], and the so-called Mott expression, S M = (π/3e)k BT∂μ[lnG(μ, T )], where G(μ, 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.