Transport in double-crossed Luttinger liquids

We study transport through two Luttinger liquids (one-dimensional electrons interacting through a Coulomb repulsion in a metal) coupled together at two points. External voltage biases are incorporated through boundary conditions. We include density-density couplings as well as single-particle hops at the contacts. For weak repulsive interactions, transport through the: wires remains undisturbed by the interwire couplings, which renormalize to zero. For strong repulsive interactions, the interwire couplings become strong. For symmetric barriers and no external voltage bias, a single gate voltage is sufficient to tune for resonance transmission in both wires. However, for asymmetric couplings or for finite external biases, the system is insulating. [S0163-1829(99)03819-9].