  We study the spin and heat conductivity of dimerized spin-1/2 chains in
homogeneous magnetic fields at finite temperatures. At zero temperature, the
model undergoes two field-induced quantum phase transitions from a dimerized,
into a Luttinger, and finally into a fully polarized phase. We search for
signatures of these transitions in the spin and heat conductivities. Using
exact diagonalization, we calculate the Drude weights, the frequency dependence
of the conductivities, and the corresponding integrated spectral weights. As a
main result, we demonstrate that both the spin and heat conductivity are
enhanced in the gapless phase and most notably at low frequencies. In the case
of the thermal conductivity, however, the field-induced increase seen in the
bare transport coefficients is suppressed by magnetothermal effects, caused by
the coupling of the heat and spin current in finite magnetic fields. Our
results complement recent magnetic transport experiments on spin ladder
materials with sufficiently small exchange couplings allowing access to the
field-induced transitions.
