  We describe the interaction of surface acoustic waves with electrons in an
array of quantum wires, patterned out of a two dimensional electron gas. Two
specific geometries are considered, in which the surface acoustic wave travels
parallel, or perpendicular to the wires. Although we assume the electron wave
functions in different wires do not overlap, the screening of the phonon
potential by the electrons in the wire array is a collective phenomenon. It is
shown that the surface acoustic wave absorption cannot be described via the ac
conductivity in the usual manner. We derive an integral equation for the
dielectric function of the electrons in the quantum wire system, and solve it
in the narrow wire approximation. Using the dielectric function we find the
absorption and the change in velocity of the surface acoustic waves.

Condensed Matter