Interaction Constants and Dynamic Conductance of a Gated Wire

We show that the interaction constant governing the long-range electron-electron interaction in a quantum wire coupled to two reservoirs and capacitively coupled to a gate can be determined by a low-frequency measurement. We present a self-consistent, charge and current conserving, theory of the full conductance matrix. The collective excitation spectrum consists of plasma modes with a relaxation rate which increases with the interaction strength and is inversely proportional to the length of the wire.