  We study the thermal transport of a spin-1/2 two leg antiferromagnetic ladder
in the direction of legs. The possible effect of spin-orbit coupling and
crystalline electric field are investigated in terms of anisotropies in the
Heisenberg interactions on both leg and rung couplings. The original spin
ladder is mapped to a bosonic model via a bond-operator transformation where an
infinite hard-core repulsion is imposed to constrain one boson occupation per
site. The Green's function approach is applied to obtain the energy spectrum of
quasi-particle excitations responsible for thermal transport. The thermal
conductivity is found to be monotonically decreasing with temperature due to
increased scattering among triplet excitations at higher temperatures. A tiny
dependence of thermal transport on the anisotropy in the leg direction at low
temperatures is observed in contrast to the strong one on the anisotropy along
the rung direction, due to the direct effect of the triplet density. Our
results reach asymptotically the ballistic regime of the spin - 1/2 Heisenberg
chain and compare favorably well with exact diagonalization data.
