Non-equilibrium transport in $d$-dimensional non-interacting Fermi gases

Understand

We consider a non-interacting Fermi gas in $d$ dimensions, both in the non-relativistic and relativistic case.

• The system of size $L^{d}$ is initially prepared into two halves $\mathcal{L}$ and $\mathcal{R}$, each of them thermalized at two different temperatures, $T_{\mathcal{L}}$ and $T_{\mathcal{R}}$ respectively.
• At time $t=0$ the two halves are put in contact and the entire system is left to evolve unitarily.
• We show that, in the thermodynamic limit, the time evolution of the particle and energy densities is perfectly described by a semiclassical approach which permits to analytically evaluate the correspondent stationary currents.