Steady States and Universal Conductance in a Quenched Luttinger Model

We obtain exact analytical results for the evolution of a 1+1-dimensional Luttinger model 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 Hλ 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 Hλ′ which differs from Hλ by the strength of the interaction. Asymptotically in time, as t→ ∞, 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 μ+- μ- between right- (+) and left- (−) moving fermions obtained from the two-point correlation function. Both I and μ+- μ- depend on λ and λ′. Only for the case λ= λ′= 0 does μ+- μ- equal the difference in the initial left and right chemical potentials. Nevertheless, the Landauer conductance for the final state, G= I/ (μ+- μ-) , has a universal value equal to the conductance quantum e2/ h for the spinless case.