Universal conductance in quantum multi-wire junctions

The subject of this thesis is the electrical conductance of rather arbitrary junctions of multiple quantum wires in the presence of electron-electron interactions. We develop a new method for calculating the conductance of these strongly-correlated junctions and we apply this method to an outstanding quantum impurity problem.;A brute force numerical calculation of conductance is not feasible for interacting junctions of more than two quantum wires. The difficulty is due to the fact that conductance is a property of an open quantum system and is related to dynamical correlation functions. Therefore, it may appear that numerical calculations of conductance require time- dependent computations in systems that are large enough to faithfully approximate open, i.e. semi-infinite, ones.;In the first half of the thesis, we derive a general relationship between the universal fixed-point conductance of quantum junctions and certain static correlation functions in appropriately constructed finite systems. The relationship is obtained within the framework of the boundary conformal field theory. The static correlation functions are shown to have a universal functional form up to a coefficient which depends on the conformally-invariant boundary condition at the junction. The universal conductance of the junction is also uniquely determined by these coefficients. Based on the formalism above, we propose a method for determining the conductance with static calculations in a closed finite system.;In the second half of the thesis, the method is applied to a Y junction of three interacting quantum wires. Extensive numerical calculations with the density matrix renormalization group method are performed to 1) verify analytical predictions that were not numerically tested before and 2) calculate the conductance of a nontrivial fixed point for which no predictions existed.;The method developed in this thesis has wide applicability to junctions with almost arbitrary structure and interactions and provides a powerful new tool for studying molecular electronic devices with strong electron-electron interaction.