system. Let us emphasise that all these results are obtained rigorously and actually hold for *any* geometry (see  \[The General System\]). These results constitute the main analytical results of this paper.

In  \[Numerical analysis\], we restrict our attention to the linear geometry represented in  \[The Quantum System\]. In analogy with the EY-model, we assume that the quantum dots are classically chaotic and consequently use random matrix theory (RMT) to describe the transport properties of the quantum dots. While we cannot prove the validity of Ohm and Fourier laws in this situation, some approximate derivations are feasible in some particular cases (see  \[Remark Amato\]). We thus turn to numerical simulations and found that Ohm and Fourier laws typically hold (in the sense of RMT) in a chain of quantum dots with self-consistent reservoirs.

The Model {#The model}
=========

We consider a chain of $N$ connected quantum dots, where each dot is coupled to a particle reservoir at temperature $T_i$ and chemical potential $\mu_i$, with $i = 1, \dots, N$. Additionally, the left and right ends of the chain are coupled to particle reservoirs with parameters ($T_\L$,$\mu_\L$) and ($T_\R$,$\mu_\R$), respectively ( \[The Quantum System\]). All these reservoirs, which we also call *terminals*, 