# Thermal and thermoelectric conductivity of Einstein-DBI system

## TL;DR

This paper computes the thermoelectric and thermal conductivities of an Einstein-DBI holographic system without translational symmetry, revealing horizon-based determination of thermal conductivity and temperature-independent ratios in specific solutions.

## Contribution

It provides a novel calculation of transport properties in Einstein-DBI systems, highlighting horizon-based thermal conductivity and temperature-independent Lorentz ratios in certain backgrounds.

## Key findings

- Thermal conductivity determined by horizon metric components in the zero dissipation limit.
- Temperature independence of Lorentz and Hall-Lorentz ratios in AdS4 at low temperatures.
- Temperature independence of these ratios in AdS2×R2 solutions.

## 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, $k^2\rightarrow 0$, 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.