  Transport of electrons through two-dimensional semiconductor structures on
the nanoscale in the presence of perpendicular magnetic field depends on the
interplay of geometry of the system, the leads, and the magnetic length. We use
a generalized master equation (GME) formalism to describe the transport through
the system without resorting to the Markov approximation. Coupling to the leads
results in elastic and inelastic processes in the system that are described to
a high order by the integro-differential equation of the GME formalism.
Geometrical details of systems and leads leave their fingerprints on the
transport of electrons through them. The GME formalism can be used to describe
both the initial transient regime immediately after the coupling of the leads
to the system and the steady state achieved after a longer time.
