situation where the input/ output site is excited and all other sites are in their ground state. In order to target exclusively fast transport that necessarily results from constructive interference, we choose $\mathcal{T} = \frac{1}{10} \frac{2\pi \hbar}{J} \frac{r_{in-out}^3}{r_{0}^3}$, [*i.e.*]{} a time-scale ten times shorter than the interval associated with direct interaction between input and output sites [@Scholak2011; @Mostarda2013]. For longer times the excitation would oscillate back and forth between input and output because the dynamics is purely coherent. With a sufficiently short time window, however, only a single oscillation is taken into consideration.

Inverse Participation Ratio (IPR)
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Under a coherent dynamics induced by a Hamiltonian of the form given in equation (\[eq:ham\]) the excitation will get delocalized over the sites of the system. This delocalization can be quantified in terms of the inverse participation ratio (IPR) defined as $$\mathrm{IPR}(t)=\frac{1}{\sum_{i=1}^{N} q_{i}^2(t)}\ ,
\label{eq:ipr}$$ where $q_i$ is the probability for site $i$ to be excited. A value for the IPR which is larger than $K-1$ implies that the excitation is delocalised over at least $K$ sites. The maximum value of the IPR is $N$, which is obtained in the case of even delocalization over the whole $N$ constituents. On the other 