Thermal Conductivity of an Ultracold Paramagnetic Bose Gas

We analytically derive the transport tensor of thermal conductivity in an ultracold, but not yet quantum degenerate, gas of Bosonic lanthanide atoms using the Chapman-Enskog procedure. The tensor coefficients inherit an anisotropy from the anisotropic collision cross section for these dipolar species, manifest in their dependence on the dipole moment, dipole orientation, and $s$-wave scattering length. These functional dependencies open up a pathway for control of macroscopic gas phenomena via tuning of the microscopic atomic interactions. As an illustrative example, we analyze the time evolution of a temperature hot-spot which shows preferential heat diffusion orthogonal to the dipole orientation, a direct consequence of anisotropic thermal conduction.