Currents in non-equilibrium steady states of open inhomogeneous $XX$-spin chains

We investigate spin and heat currents in the non-equilibrium steady state of inhomogeneous $XX$-spin chains, which act as interfaces between two bosonic heat baths. Using special functions that diagonalize the single-particle Hamiltonian, we derive closed-form expressions for these currents. For small temperature differences between the baths, we show that inhomogeneities breaking the mirror symmetry of the chain significantly reduce both heat and spin conductivities. Connections with perfect state transfer are discussed.