, Volume 319, Issue 2, pp 501-513
Date: 04 Dec 2012

Landauer-Büttiker Formula and Schrödinger Conjecture

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Abstract

We study the entropy flux in the stationary state of a finite one-dimensional sample \({\mathcal{S}}\) connected at its left and right ends to two infinitely extended reservoirs \({\mathcal{R}_{l/r}}\) at distinct (inverse) temperatures \({\beta_{l/r}}\) and chemical potentials \({\mu_{l/r}}\) . The sample is a free lattice Fermi gas confined to a box [0, L] with energy operator \({h_{\mathcal{S}, L}= - \Delta + v}\) . The Landauer-Büttiker formula expresses the steady state entropy flux in the coupled system \({\mathcal{R}_l + \mathcal{S} + \mathcal{R}_r}\) in terms of scattering data. We study the behaviour of this steady state entropy flux in the limit \({L \to \infty}\) and relate persistence of transport to norm bounds on the transfer matrices of the limiting half-line Schrödinger operator \({h_\mathcal{S}}\) .

Communicated by B. Simon