Off-critical Luttinger junctions

We investigate Luttinger junctions of quantum wires away from criticality. The one-body scattering matrix, corresponding to the off-critical boundary conditions at the junction, admits, in general, antibound and/or bound states. Their contribution to the theory is fixed by causality. The presence/absence of bound states determines the existence of two different regimes with inequivalent physical properties. A scattering matrix without bound states defines an isolated equilibrium system. Bound states instead drive the system away from equilibrium, giving raise to nontrivial incoming or outgoing energy flows in the junction. We derive in both regimes and in explicit form the electromagnetic conductance tensor, pointing out the different impacts of bound and antibound states.