A Geometric Approach to the Landauer-Büttiker Formula

Rym Ben Sâad (1) , Claude-Alain Pillet (2, 3, 4)

1 Laboratoire Mathématiques et Applications, INSAT, Tunis
2 FRUMAM - Fédération de Recherche des Unités de MAthématiques de Marseille
3 CPT - E5 Physique statistique et systèmes complexes
4 CPT - Centre de Physique Théorique - UMR 7332

We consider an ideal Fermi gas confined to a geometric structure consisting of a central region -- the sample -- connected to several infinitely extended ends -- the reservoirs. Under physically reasonable assumptions on the propagation properties of the one-particle dynamics within these reservoirs, we show that the state of the Fermi gas relaxes to a steady state. We compute the expected value of various current observables in this steady state and express the result in terms of scattering data, thus obtaining a geometric version of the celebrated Landauer-Büttiker formula.

Mots clés: nonequilibrium steady state; scattering theory; quantum transport; nonequilibrium statistical mechanics

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Mécanique statistique [cond-mat.stat-mech]

Rym Ben Sâad, Claude-Alain Pillet. A Geometric Approach to the Landauer-Büttiker Formula. Journal of Mathematical Physics, 2014, 55, pp.075202. ⟨10.1063/1.4879238⟩. ⟨hal-00943060⟩