Thermal and thermoelectric conductivity of Einstein-DBI system

We calculate the thermoelectric and thermal conductivity of Einstein-DBI system without the translational symmetry. We show that strictly, the longitudinal component of the thermal conductivity in the vanishing dissipation limit, $k^2\rightarrow 0$, is determined only by the metric components evaluated at the horizon of the black hole in the same limit. The temperature dependence of the transport quantities are obtained for $AdS_4$ and $AdS_2\times R^2$ solutions. The Lorentz ratio and Hall-Lorentz ratio are found to be independent of temperature for $AdS_4$ solution in the low temperature limit, whereas the above mentioned quantities are independent of temperature for $AdS_2\times R^2$ solution.