Wave localization in complex networks with high clustering

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.