Diffusive geodesics wandering in networks of rigid chains

Area of Science:

• Physics
• Network Science
• Statistical Mechanics

Background:

• Standard network models often overlook directional correlations between bonds.
• Understanding transport properties in complex spatial networks is crucial.
• Existing bounds for random spatial networks may not apply universally.

Purpose of the Study:

• To introduce a new ensemble of spatial networks incorporating directional correlations.
• To investigate the transport properties and geodesic behavior of these novel networks.
• To explore the implications for universality classes in Euclidean first-passage percolation.

Main Methods:

• Constructing spatial networks from junctions of hindered-rotation chains.
• Analyzing geodesic paths and their wandering exponents (ξ).
• Examining travel-time fluctuations (χ) and transverse deviations.

Main Results:

• Emergent networks support geodesics with ξ=1/2 and χ=0, aligning with the Kardar-Parisi-Zhang (KPZ) relation.
• Observed χ=0 violates the predicted bound of χ≥1/8 in Poissonian frameworks.
• Transverse deviations follow the Kolmogorov distribution, linking to Brownian bridge excursions.

Conclusions:

• These findings establish a new universality class for Euclidean first-passage percolation.
• Local orientational memory in networks significantly alters transport properties.
• The study challenges established bounds for random spatial networks and highlights the importance of bond correlations.