Alternating-Current Conductivity for a Two-Channel Interacting Quantum Wire

We investigate theoretically the ac conductivity of a clean two-channel spinless quantum wire in the presence of both short-ranged intra- and inter-channel electron--electron interactions. In the Luttinger-liquid regime, we formulize the action functional of the system with an external time-varying
electric field. The obtained expression of ac conductivity for the system within linear response theory is generally an oscillation function of the interaction strength, the driving frequency as well as the measured position in the wire. The numerical examples demonstrate that the amplitude of ac conductivity is renormalized by the both interactions, and the dc conductivity of the system with inter-channel interaction is smaller than that without inter-channel interaction.