Diffusive geodesics wandering in networks of rigid chains

TL;DR

This paper introduces a new class of spatial networks with correlated edges, revealing unique geodesic behaviors and challenging existing bounds in Euclidean first-passage percolation, thus expanding understanding of transport in complex media.

Contribution

It presents a novel ensemble of spatial networks with directional correlations, demonstrating a new universality class with distinct geodesic and fluctuation properties.

Findings

Geodesics exhibit a wandering exponent of 1/2.

Travel-time fluctuations are consistent with KPZ but violate the Poissonian bound.

Transverse deviations follow the Kolmogorov distribution.

Abstract

We introduce an ensemble of spatial networks built from the junctions of hindered-rotation chains, incorporating directional correlations between bonds, an aspect ignored in the standard network modeling paradigm. The emergent random networks support geodesics with a wandering exponent $\xi = 1/2$, and a travel-time fluctuation exponent $\chi = 0$, consistent with the KPZ relation, yet violating the bound~$\chi\geq1/8$ predicted in the Poissonian framework. Transverse deviations follow the Kolmogorov distribution, indicating similarities between Brownian bridge excursions and geodesics in a random medium with correlated edges orientations. These results reveal a new universality class of Euclidean first-passage percolation, where local orientational memory reshapes transport properties and challenges existing bounds for random spatial networks.