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| HAL : hal-00660165, version 3 |
| DOI : 10.1007/s00220-012-1628-3 |
| Fiche détaillée |  Récupérer au format |
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| Communications in Mathematical Physics 319 (2012) 501-513 |
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| Versions disponibles : | v1 (17-01-2012) | v2 (17-07-2012) | v3 (05-04-2013) |
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| Landauer-Büttiker formula and Schrödinger conjecture |
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| Laurent Bruneau 1Vojkan Jaksic 2 |
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| (04/12/2012) |
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| We study the entropy flux in the stationary state of a finite one-dimensional 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 Landauer-Büttiker 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 half-line Schrödinger 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 Schrödinger conjecture in spectral theory of one-dimensional Schrödinger operators, thus giving a physically appealing interpretation to the Schrödinger conjecture. |
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| 1 : | Laboratoire d'Analyse, Géométrie et Modélisation (AGM) |
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CNRS : UMR8088 – Université de Cergy Pontoise |
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| 2 : | Department of Mathematics and Statistics [Mac Gill] |
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Mac Gill University |
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| 3 : | Centre de Physique Théorique (CPT) |
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CNRS : UMR7332 – Aix-Marseille Université - AMU – Université Sud Toulon Var |
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| Domaine | : | Physique/Physique mathématique Mathématiques/Physique mathématique Physique/Matière Condensée/Mécanique statistique Physique/Matière Condensée/Science des matériaux |
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| nonequilibrium statistical mechanics – quantum transport – nonequilibrium steady states – spectral theory – Schrödinger conjecture |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00660165, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00660165 | |
| oai:hal.archives-ouvertes.fr:hal-00660165 | |
| Contributeur : Claude-Alain Pillet | |
| Soumis le : Mercredi 3 Avril 2013, 22:45:29 | |
| Dernière modification le : Vendredi 5 Avril 2013, 15:11:20 | |
