  Simple exclusion processes for particles moving along two parallel lattices
and jumping between them are theoretically investigated for asymmetric rates of
transition between the channels. An approximate theoretical approach, that
describes the particle dynamics exactly in any vertical cluster of two parallel
sites and neglects the correlations between the different vertical clusters, is
applied to calculate stationary-state density profiles, currents and phase
diagrams. Surprisingly, it is found that asymmetry in the coupling between the
channels leads to a very complex phase behavior that is very different from
two-channel simple exclusion processes with symmetric coupling. There are seven
stationary-state phases in the simple exclusion processes with asymmetric
transition rates between the channels, in contrast to three phases found for
the systems with symmetric coupling. In addition, a new maximal-current phase
with a domain wall in the middle of the lattices, that has no analogs in other
exclusion processes, is observed. Although the explicit calculations are
presented only for the case of full asymmetry, when the particles can only jump
between the channels in one direction, the properties of two-channel simple
exclusion systems with general asymmetry are also discussed. Theoretical
predictions are in excellent agreement with extensive computer Monte Carlo
simulations.
