  Quantum systems can undergo phase transitions and show distinct features in
different phases. The corresponding transport properties can also vary
significantly due to the underlying quantum phase. We investigate the transport
behaviour of a two-legged bosonic ladder in a uniform gauge field, which is
known to have a Meissner-like phase and a vortex phase in the absence of
dissipation. The ladder is coupled to bosonic baths at different temperatures,
and we study it using the non-equilibrium Green's function method. In
particular, we show the presence of a chiral current and how it is affected by
the temperature bias and the dissipation strength. We also demonstrate that the
opening of a gap between the lower and upper energy band results in the
possibility of tuning heat and particle transport through the ladder. We show
that for system parameters for which the ground state is in a vortex phase, the
system is more sensitive to external perturbations.
