Transmission through correlated fermion systems and size of the corresponding effective one-body scatterer
Résumé
In order to extend the Landauer formulation of quantum transport to spinless correlated fermions, we consider a system in which charge carriers interact, connected to two reservoirs by non-interacting one-dimensional leads. We study the size of the attached leads necessary for reducing this many-body scatterer to an effective one-body scatterer with interaction-dependent parameters. To obtain this size, we consider two identical correlated systems connected by a non-interacting lead of length $L_\mathrm{C}$. We demonstrate that the effective one-body transmission of the ensemble deviates by an amount $A/L_\mathrm{C}$ from the behavior obtained assuming an effective one-body description for each element and the combination law of scatterers in series. $A$ is maximum for the interaction strength $U$ around which the Luttinger liquid becomes a Mott insulator in the used model, and vanishes when $U \to 0$ and $U \to \infty$. Analogies with the Kondo problem are pointed out.