  Nanoscale electronic transport is of intense technological interest, with
applications ranging from semiconducting devices and molecular junctions to
charge migration in biological systems. Most explicit theoretical approaches
treat transport using a combination of density functional theory (DFT) and
non-equilibrium Green's functions. This is a static formalism, with dynamic
response properties accommodated only through complicated extensions. To
circumvent this limitation, the carrier density may be propagated using
real-time time-dependent DFT (RT-TDDFT), with boundary conditions corresponding
to an open quantum system. Complex absorbing potentials can emulate outgoing
particles at the simulation boundary, although these do not account for
introduction of charge density. It is demonstrated that the desired positive
particle flux is afforded by a class of $\mathcal{PT}$-symmetric generating
potentials that are characterized by anisotropic transmission resonances. These
potentials add density every time a particle traverses the cell boundary, and
may be used to engineer a continuous pulse train for incident packets. This is
a first step toward developing a complete transport formalism unique to
RT-TDDFT.
