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

Turnstile pumping through an open quantum wire