Temperature Dependence of the Thermal Conductivity of a Trapped Dipolar Bose-Condensed Gas

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The thermal conductivity of a trapped dipolar Bose condensed gas is calculated as a function of temperature in the framework of linear response theory. The contributions of the interactions between condensed and noncondensed atoms and between noncondensed atoms in the presence of both contact and dipole-dipole interactions are taken into account to the thermal relaxation time, by evaluating the self-energies of the system in the Beliaev approximation. We will show that above the Bose-Einstein condensation temperature (T > T BEC ) in the absence of dipole-dipole interaction, the temperature dependence of the thermal conductivity reduces to that of an ideal Bose gas. In a trapped Bose-condensed gas for temperature interval k B T << n 0 g B , E p << k B T (n 0 is the condensed density and g B is the strength of the contact interaction), the relaxation rates due to dipolar and contact interactions between condensed and noncondensed atoms change as $$ {\tau}_{dd12}^{-1}\propto {e}^{-E/{k}_BT} $$ and τ c12 ∝ T −5, respectively, and the contact interaction plays the dominant role in the temperature dependence of the thermal conductivity, which leads to the T −3 behavior of the thermal conductivity. In the low-temperature limit, k B T << n 0 g B , E p >> k B T, since the relaxation rate $$ {\tau}_{c12}^{-1} $$ is independent of temperature and the relaxation rate due to dipolar interaction goes to zero exponentially, the T 2 temperature behavior for the thermal conductivity comes from the thermal mean velocity of the particles. We will also show that in the high-temperature limit (k B T > n 0 g B ) and low momenta, the relaxation rates $$ {\tau}_{c12}^{-1} $$ and $$ {\tau}_{dd12}^{-1} $$ change linearly with temperature for both dipolar and contact interactions and the thermal conductivity scales linearly with temperature.