will be solved only in the linear response approximation. Then we will work out the remaining electric and heat currents: $I_\L = - I_\R$ and $J_\L = - J_\R$ (these equalities are satisfied in the linear response regime; see  \[remark heat\]). Observe that in this situation, charge and heat dissipation occurs mostly at the left and right boundaries of the system. Indeed, due to the self-consistency condition, the dissipation occurs at first order at the boundaries while at most as second order effects along the system.

Up to that point, the system is described by any scattering matrix $S$ and has therefore no specific geometry (see  \[The General System\]). In order to obtain a system with the *linear* geometry represented in  \[The Quantum System\], and to interpret $I_\L$ and $J_\L$ as the currents flowing through the system, from left to right, we will consider that the *global* scattering matrix $S$ is given in terms of the *local* (linearly ordered) scattering matrices, $S^{(1)},\dots,S^{(N)}$, associated to the $N$ quantum dots.

In  \[Numerical analysis\], we will study numerically the properties of the *composite* scattering matrix $S$, using random matrix theory (RMT), and show that the currents through the chain of quantum dots with 