FM 5-16 https://arxiv.org/abs/1511.01884 (Comm. Math. Phys. http://link.springer.com/article/10.1007/s00220-016-2631-x)

Author : Edwin Langmann, Joel L. Lebowitz, Vieri Mastropietro, Per Moosavi

Title: Steady states and universal conductance in a quenched Luttinger model

Abstract: We obtain exact analytical results for the evolution of a 1+1-dimensional Luttinger model H_l prepared in a domain wall initial state, i.e., a state with different densities on its left and right sides. Such an initial state is modeled as the ground state of a translation invariant Luttinger Hamiltonian with short range non-local interaction and different chemical potentials to the left and right of the origin. The system evolves for time t > 0 via a Hamiltonian H_l which differs from H_l’ by the strength of the interaction. Asymptotically in time, after taking the thermodynamic limit,the system approaches a translation invariant steady state. This final steady state carries a current I and has an effective chemical potential difference between right- (+) and left- (−) moving fermions obtained from the two-point correlation function. The Landauer conductance for the final state, has a universal value equal to the conductance quantum.

Keywords: Landauer conducatance, domain wall, NESS.