A geometric approach to the Landauer-Büttiker formula

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-Buttiker formula.