  The effect of a perpendicular magnetic field on the quantized current induced
by a surface acoustic wave in a quasi-1D channel is studied. The channel has
been produced experimentally in a GaAs heterostructure by shallow etching
techniques and by the application of a negative gate voltage to Schottky split
gates. Commensurability oscillations of the quantized current in this
constriction have been observed in the interval of current between quantized
plateaus. The results can be understood in terms of a moving quantum dot with
the electron in the dot tunneling into the adjacent two-dimensional region. The
goal is to explain qualitatively the mechanism for the steplike nature of the
acoustoelectric current as a function of gate voltage and the oscillations when
a magnetic field is applied. A transfer Hamiltonian formalism is employed.
