  We study Landau-Zener transitions in a fermionic dissipative environment
where a two-level (up and down states) system is coupled to two metallic leads
kept with different chemical potentials at zero temperature. The dynamics of
the system is simulated by an iterative numerically exact influence functional
path integral method. In the pure Landau-Zener problem, two kinds of transition
(from up to down state and from down to up state) probability are symmetric.
However, this symmetry is destroyed by coupling the system to the bath. In
addition, in both kinds of transitions, there exists a nonmonotonic dependence
of the transition probability on the sweep velocity; meanwhile nonmonotonic
dependence of the transition probability on the system-bath coupling strength
is only shown in one of them. As in the spin-boson model, these phenomena can
be explained by a simple phenomenological model.
