Many-particle correlations in a non-equilibrium Luttinger liquid

Abstract

We develop an operator-based approach to the problem of a Luttinger liquid conductor in anon-equilibrium stationary state. We show that the coherent-state many-bodyfermionic density matrix and all fermionic correlation functions out of equilibrium aregiven by one-dimensional functional determinants of the Fredholm type. Thus,the model constitutes a remarkable example of a many-body problem where allthe correlation functions can be evaluated exactly. On the basis of the generalformalism, we investigate four-point correlation functions of the fermions comingout of the Luttinger liquid wire. The correlations obtained among the fermionicdistribution functions represent the combined effect of interaction and non-equilibriumconditions.