  We use a non-Markovian generalized master equation (GME) to describe the
time-dependent charge transfer through a parabolically confined quantum wire of
a finite length coupled to semi-infinite quasi two-dimensional leads. The
quantum wire and the leads are in a perpendicular external magnetic field. The
contacts to the left and right leads depend on time and are kept out of phase
to model a quantum turnstile of finite size. The effects of the driving period
of the turnstile, the external magnetic field, the character of the contacts,
and the chemical potential bias on the effectiveness of the charge transfer of
the turnstile are examined, both in the absence and in the presence of the
magnetic field. The interplay between the strength of the coupling and the
strength of the magnetic field is also discussed. We observe how the edge
states created in the presence of the magnetic field contribute to the pumped
charge.
