Quantum transport in the flux rhombic lattice

We analyse stationary current of the bosonic particles in the flux rhombic lattice connecting two particle reservoirs. For vanishing inter-particle interactions the current is shown to monotonically decrease as the flux is increased and become strictly zero for the Peierls phase equal to $\pi$. Non-zero interactions modify this dependence and for moderate interaction strength the current is found to be independent of the flux value.