  We study Landau-Zener transitions between two states with the addition of a
shared discretized continuum. The continuum allows for population decay from
the initial state as well as indirect transitions between the two states. The
probability of nonadiabatic transition in this multichannel model preserves the
standard Landau-Zener functional form except for a shift in the usual
exponential factor, reflecting population transfer into the continuum. We
provide an intuitive explanation for this behavior assuming independent
individual transitions between pairs of states. In contrast, the probability of
survival in the ground state at long time shows a novel, non-monotonic,
functional form, with an oscillatory behavior in the sweep rate at low sweep
rate values. We contrast the behavior of this open-multistate model to other
generalized Landau-Zener models incorporating an environment: the stochastic
Landau-Zener model and the dissipative case, where energy dissipation and
thermal excitations affect the adiabatic region. Finally, we present evidence
that the continuum of states may act to shield the two-state Landau-Zener
transition probability from the effect of noise.
