Critical properties of cluster size distribution in an asymmetric diffusion-aggregation model

Area of Science:

• Statistical mechanics
• Condensed matter physics
• Theoretical physics

Background:

• Hard-core particles exhibit complex dynamics in confined systems.
• Understanding cluster formation and size distribution is crucial for predicting system behavior.

Purpose of the Study:

• To investigate the stochastic dynamics of diffusing hard-core particles on a periodic chain.
• To analyze the cluster size distribution in the long time limit as a function of particle concentration.
• To identify critical phenomena and scaling laws governing cluster formation.

Main Methods:

• Development of a stochastic dynamics model with asymmetric diffusion rules.
• Application of Smoluchowski's theory for cluster merging and fragmentation.
• Utilizing a time-dependent master equation and generating functions for analysis.
• Focusing on the large size limit and steady-state conditions.

Main Results:

• The model allows for the creation of particle clusters of varying sizes.
• A critical particle density (c* = sqrt(2)-1) was identified.
• At this critical density, the cluster size distribution exhibits a power-law decay with an exponent of 5/2.

Conclusions:

• The identified critical density and power-law exponent provide key insights into the phase transitions of particle systems.
• The stochastic dynamics model successfully captures emergent cluster behaviors.
• Further research can explore variations in dimensionality and particle interactions.