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Related Experiment Video

Updated: Jun 28, 2026

Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms

Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms

Published on: November 1, 2019

Wave localization in complex networks with high clustering.

Lukas Jahnke¹, Jan W Kantelhardt, Richard Berkovits

¹Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany.

Physical Review Letters

|November 13, 2008

Summary

This summary is machine-generated.

Strong network clustering can cause quantum phase transitions in coherent excitations, like light wave packets in optical networks. Exceeding a triangle closure threshold halts wave propagation, a phenomenon feasible with current technology.

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Area of Science:

Complex networks
Quantum physics
Optical systems

Background:

Complex networks exhibit link clustering, influencing emergent phenomena.
Quantum phase transitions, such as Anderson localization, are critical in disordered systems.
Coherent excitations in optical networks are sensitive to network topology.

Purpose of the Study:

To investigate the impact of network clustering on quantum phase transitions.
To explore the conditions under which coherent excitation propagation is inhibited.
To map the phase diagram of these transitions in scale-free networks.

Main Methods:

Analyzing the relationship between triadic closure (clustering) and quantum phase transitions.
Modeling light wave packet propagation in optical networks.
Determining phase diagrams for scale-free networks with varying degree distributions (P(k) ~ k{-lambda}) and disorder.

Main Results:

High link clustering induces a quantum phase transition (localization-delocalization) for coherent excitations.
A threshold in the fraction of closed triangles can halt light wave packet propagation in optical networks.
Disorder reduces the critical clustering coefficient required for phase transitions, broadening the parameter space for transitions.

Conclusions:

Strong network clustering is a key factor in Anderson-like quantum phase transitions.
Optical network experiments can demonstrate this phenomenon, feasible with current technology.
The interplay between clustering, disorder, and network degree distribution governs the occurrence of these transitions.