Landauer-Buttiker Formula and Schrodinger Conjecture

We study the entropy flux in the stationary state of a finite one-dimensional sample connected at its left and right ends to two infinitely extended reservoirs at distinct (inverse) temperatures and chemical potentials . The sample is a free lattice Fermi gas confined to a box [0, L] with energy operator . The Landauer-Buttiker formula expresses the steady state entropy flux in the coupled system in terms of scattering data. We study the behaviour of this steady state entropy flux in the limit and relate persistence of transport to norm bounds on the transfer matrices of the limiting half-line Schrodinger operator .