Thermal and thermoelectric conductivity of Einstein-DBI system

Abstract

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, $k^2\to 0$, 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 $Ad{S}_4$ and $Ad{S}_2\times R^2$ solutions. The Lorentz ratio and Hall-Lorentz ratio are found to be independent of temperature for $Ad{S}_4$ solution in the low temperature limit, whereas the above mentioned quantities are independent of temperature for $Ad{S}_2\times R^2$ solution.

1+31 pages, 6 figures, Typos corrected and 3 new figures added