The assembly of nanometer material structures, at scales intermediate between those of condensed matter and atomic systems, brings the promise of revolutionary new devices. But at the same time, many fundamental science problems are brought out into light, such as how to describe the collective quantum behavior of interacting electrons when they are confined to geometries at the nanometer scale. In this research work, I address a number of basic science questions that pertain to problem of interconnection and integration of nano-circuits.

 

In this work, we investigate Y-junctions of three quantum wires, attached to a ring through which magnetic flux can be inserted. These Y-junctions are the simplest systems with a fermion sign problem.