A Geometric Approach to the Landauer-B\"uttiker Formula
Mathematical Physics
2014-02-07 v1 Statistical Mechanics
math.MP
Quantum Physics
Abstract
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-B\"uttiker formula.
Keywords
Cite
@article{arxiv.1402.1480,
title = {A Geometric Approach to the Landauer-B\"uttiker Formula},
author = {R. Ben Sâad and C. -A. Pillet},
journal= {arXiv preprint arXiv:1402.1480},
year = {2014}
}