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. The interaction parameter is determined by the first two coefficients of the out-of-phase component of the dynamic conductance measured at the gate.