  The degenerate Bose-Fermi (BF) mixtures in one dimension present a novel
realization of two decoupled Luttinger liquids with bosonic and fermionic
degrees of freedom at low temperatures. However, the transport properties of
such decoupled Luttinger liquids of charges have not yet been studied. Here we
apply generalized hydrodynamics to study the transport properties of
one-dimensional (1D) BF mixtures with delta-function interactions. The initial
state is set up as the semi-infinite halves of two 1D BF mixtures with
different temperatures, joined together at the time $t=0$ and the junction
point $x=0$. Using the Bethe ansatz solution, we first rigorously prove the
existence of conserved charges for both the bosonic and fermionic degrees of
freedom, preserving the Euler-type continuity equations. We then analytically
obtain the distributions of the densities and currents of the local conserved
quantities which solely depend on the ratio $\xi=x/t$. The left and right
moving quasiparticle excitations of the two halves form multiple segmented
light-cone hydrodynamics that display ballistic transport of the conserved
charge densities and currents in different degrees of freedom. Our analytical
results provide a deep understanding of the quantum transport of
multi-component Luttinger liquids in quantum systems with both bosonic and
fermionic statistics.
