  We investigate the coherent dynamics of a non-interacting Bose-Einstein
condensate in a system consisting of two bosonic reservoirs coupled via a
spatially localized mode. We describe this system by a two-terminal
Fano-Anderson model and investigate analytically the time evolution of
observables such as the bosonic Josephson current. In doing so, we find that
the Josephson current sensitively depends on the on-site energy of the
localized mode. This facilitates to use this setup as a transistor for a
Bose-Einstein condensate. We identify two regimes. In one regime, the system
exhibits well-behaved long-time dynamics with a slowly oscillating and undamped
Josephson current. In a second regime, the Josephson current is a superposition
of an extremely weakly damped slow oscillation and an undamped fast
oscillation. Our results are confirmed by finite-size simulations.
