Possibility of interpreting amorphicity as spatial chaos

In order to gain insight into whether amorphicity can be interpreted as spatial chaos, we investigate one-dimensional chaotic configurations of atoms. These configurations are generated by the Baker transformation or, equivalently, by the Bernoulli shift, which is characteristic for chaos. We show that the distribution function $G_j$ of the $j$th nearest-neighbor distances of these configurations is asymptotically (as $j\to \infty$) a Gaussian distribution with a width growing as $\sqrt{j}$ (local limit theorem). Furthermore, the pair distribution function $G$ exhibits peaks related to the positions of nearby atoms, but in the limit of large distances these oscillations go to zero, and the pair distribution function converges to a constant, as expected for amorphous solids.