  Recent conductivity measurements performed on the hole-doped two-leg ladder
material $\mathrm{Sr_{14-x}Ca_xCu_{24}O_{41}}$ reveal an approximately linear
power law regime in the c-axis DC resistivity as a function of temperature for
$x=11$. In this work, we employ a bosonic model to argue that umklapp processes
are responsible for this feature and for the high spectral weight in the
optical conductivity which occurs beyond the finite frequency Drude-like peak.
Including quenched disorder in our model allows us to reproduce experimental
conductivity and resistivity curves over a wide range of energies. We also
point out the differences between the effect of umklapp processes in a single
chain and in the two-leg ladder.
