  In quasiballistic semiconductor nanostructures, carrier exchange between the
active region and dissipative contacts is the mechanism that governs
relaxation. In this paper, we present a theoretical treatment of transient
quantum transport in quasiballistic semiconductor nanostructures, which is
based on the open system theory and valid on timescales much longer than the
characteristic relaxation time in the contacts. The approach relies on a model
interaction between the current-limiting active region and the contacts, given
in the scattering-state basis. We derive a non-Markovian master equation for
the irreversible evolution of the active region's many-body statistical
operator by coarse-graining the exact dynamical map over the contact relaxation
time. In order to obtain the response quantities of a nanostructure under bias,
such as the potential and the charge and current densities, the non-Markovian
master equation must be solved numerically together with the Schr\"{o}dinger,
Poisson, and continuity equations. We discuss how to numerically solve this
coupled system of equations and illustrate the approach on the example of a
silicon nin diode.
