Laboratoire de Physique Théorique
Toulouse - UMR 5152

The linear response theory is a cornerstone of the quantum theory. It allows to derive extremely useful formulas such as the Kubo formula or the Fluctuation-Dissipation Theorem (FDT) which are extensively used in all fields. It is usually believed to be restricted to weak perturbations, such as an electric field. We have shown that this belief is wrong : we have indeed developed a general approach based on a non-linear extension of Kubo formula, capable of addressing the non-equilibrium situation and to include interactions without the restrictions found in previous works. Even though these results are not restricted to condensed matter theory, we choose here to apply them to develop a novel transport framework for arbitrary mesoscopic systems connected to two or many terminals. We show that this solves subtleties which have been a subject of debates since the development of the scattering approach. We express the conductance matrix in a microscopic way, which obeys the current conservation and jauge invariance. We believe this is an important achievement not only for time-dependent voltages or/and Hamiltonian ; It is already crucial for the stationary regime, as the scattering approach is not suited to deal with interacting or/and non-linear systems.

We demonstrate the practical interest of this work by showing how it elegantly clarifies issues on the asymmetry and sign of the excess noise recently measured in experiments. Finally, in the case of a tunnel junction we obtain a non-perturbative out-of-equilibrium link between conductance and current fluctuations (valid including in interacting systems), and derive a universal property of the finite frequency noise in the perturbative regime. References :

I. Safi, http://arxiv.org/abs/0908.4382 I. Safi and P. Joyez, Phys. Rev. B 84, 205129 (2011)