where exactly the information on the dynamical localization is hidden: Is it determined by the spectral properties of the Laplacian matrix, or is it mostly coded in the entries of the matrix $G$ composed from the eigenvectors of $L$? To understand this we compare the behavior of a one-dimensional system of $N$ sites with the one of its three-dimensional analogue, where dynamical localization is absent [@Fontes1999]. The total number of sites shall also be $N$, i.e. the side length of the cube is $N^{1/3}$. The rates for the 3D case are as follows: $$\begin{aligned}
    w_{k\rightarrow l}^{(3)} &= \begin{cases}
                          -1/\tau_k, &\text{if~} k = l,\\
                          1/(6\tau_k), &\text{if~} k,l \text{~neighbors},\\
                          0, &\text{else}.
                        \end{cases}\end{aligned}$$ A comparison between the disorder averaged evolution of $Y_2$ on the one- and three-dimensional case is shown in Fig. \[fig:Y21D3D\]. As Fontes *et al.* [@Fontes1999] proved, there is no dynamical localization in the 3D case, i.e. $\lim_{t\rightarrow \infty} \lim_{N \rightarrow \infty} \langle Y_2\rangle_\tau = 0$, which, for finite lattices with site number $N$, can be understood as $\lim_{N \rightarrow \infty} \min_t \langle Y_2\rangle_\tau = 0$. In Fig. \[fig:Y21D3D\] this can be seen by the fact that $\min_t\langle Y_2^{3D}\rangle_\tau$ is of the order of $N^{-1}$ and $\min_t\langle Y_2^{1D}\rangle_\tau$ is considerably larger 