  We investigate quantum transport of electrons, phase solitons, etc. through
mesoscopic networks of zero-dimensional quantum dots. Straight and circular
ladders are chosen as networks with each coupled with three semi-infinite leads
(with one incoming and the other two outgoing). Two transmission probabilities
(TPs) as a function of the incident energy $\epsilon$ show a transition from
anti-phase aperiodic to degenerate periodic spectra at the critical energy
$\epsilon_c$ which is determined by a bifurcation point of the bulk energy
dispersions. TPs of the circular ladder depend only on the parity of the
winding number. Introduction of a single missing bond (MB) or missing step
doubles the period of the periodic spectra at $\epsilon>\epsilon_c$ . Shift of
the MB by lattice constant results in a striking switching effect at
$\epsilon<\epsilon_c$. In the presence of the electric-field induced spin-orbit
interaction (SOI), an obvious spin filtering occurs against the
spin-unpolarized injection. Against the spin-polarized injection, on the other
hand, the spin transport shows spin-flip (magnetization reversal) oscillations
with respect to SOI. We also show a role of soliton in the context of its
transport through the ladder networks.
