  A theory of d.c. electric current induced in a quantum channel by a
propagating surface acoustic wave (acoustoelectric current) is worked out. The
first observation of the acoustoelectric current in such a situation was
reported by J. M. Shilton et al., Journ. Phys. C (to be published). The authors
observed a very specific behavior of the acoustoelectric current in a
quasi-one-dimensional channel defined in a GaAs-AlGaAs heterostructure by a
split-gate depletion -- giant oscillations as a function of the gate voltage.
Such a behavior was qualitatively explained by an interplay between the
energy-momentum conservation law for the electrons in the upper transverse mode
with a finite temperature splitting of the Fermi level. In the present paper, a
more detailed theory is developed, and important limiting cases are considered.
