The influence of a longitudinal magnetic field on the Coulomb drag current created in the ballistic transport regime in a quantum well by a ballistic current in a nearby parallel quantum well is investigated. We consider the case where the magnetic field is so strong that the Larmour radius is smaller than the width of the well. Both in Ohmic and non-Ohmic case, sharp oscillations of the drag current as a function of the gate voltage or chemical potential are predicted. We also study dependence of the drag current on the voltage $V$ across the driving wire, as well as on the magnetic field $B$. Studying the Coulomb drag one can make conclusions about the electron spectrum and and electron-electron interaction in quantum wells.
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