Resonant multilead point-contact tunneling

We analyze a model of resonant point-contact tunneling between multiple Lut tinger-liquid leads. The model is a variant of the multichannel Kondo model and can be related to the quantum Brownian motion of a particle on lattice s with pi flux through each plaquette (in the three-lead case, it is a hone ycomb lattice with pi flux). By comparing the perturbative and instanton ga s expansions, we find a duality property of the model. At the boundary, thi s duality exchanges Neumann and Dirichlet boundary conditions on the Tomona ga-Luttinger bosons, which describe the leads; in the bulk, it exchanges th e "momentum'' and "winding" modes of these bosons. Over a certain range of Luttinger-liquid parameter g, a nontrivial intermediate coupling fixed-poin t controls the low-energy physics. The finite conductance at this fixed poi nt can be exactly computed for two special values of g. For larger values o f g, there is a stable fixed point at strong coupling that has enhanced con ductance resulting from an analogue of Andreev reflection at the point cont act. [S0163-1829(99)06023-3].