 1276 L. Bruneau, V. Jaksic, C.A. Pillet
 LandauerBuettiker formula and Schroedinger conjecture
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Jul 16, 12

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Abstract. We study the entropy flux in the stationary state of a finite onedimensional sample S connected at its left and right ends to two infinitely extended reservoirs at distinct temperatures T1, T2 and chemical potentials mu1, mu2. The sample is a free lattice Fermi gas confined to a box [0, L] with energy operator \Delta + v. The LandauerBuettiker formula expresses the steady state entropy flux in the coupled system in terms of scattering data. We study the behavior of this steady state entropy flux in the limit L>infinity and relate persistence of transport to norm bounds on the transfer matrices of the limiting halfline Schroedinger operator h. A natural conjecture is that the set of energies at which transport persists in this limit is precisely the essential support of the absolutely continuous spectrum of h. We show that this conjecture is equivalent to the Schroedinger conjecture in spectral theory of onedimensional Schroedinger operators, thus giving a physically appealing interpretation to the Schroedinger conjecture.
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