Interaction of surface acoustic waves with an array of quantum wires

We describe the interaction of surface acoustic waves with electrons in an array of quantum wires, patterned out of a two-dimensional electron gas. Tw o specific geometries are considered, in which the surface acoustic wave tr avels parallel, or perpendicular to the wires. Although we assume the elect ron wave functions in different wires do not overlap, the screening of the phonon potential by the electrons in the wire array is a collective phenome non. It is shown that the surface acoustic wave absorption cannot be descri bed via the ac conductivity in the usual manner. We derive an integral equa tion for the dielectric function of the electrons in the quantum wire syste m, and solve it in the random phase approximation and in the narrow wire ap proximation. Using the dielectric function we find the absorption and the c hange in velocity of the surface acoustic waves.