A+A→∅ model with a bias towards nearest neighbor.

Area of Science:

• Statistical Physics
• Reaction-Diffusion Systems
• Complex Systems

Background:

• The A+A→∅ reaction-diffusion model describes systems where particles annihilate upon encountering each other.
• Understanding particle spacing and dynamics is crucial in various physical and biological processes.

Purpose of the Study:

• To investigate the effect of a local spatial and temporal bias (ε) on the A+A→∅ reaction-diffusion model on a ring.
• To determine how this bias influences the universality class and scaling behavior of the system.

Main Methods:

• Analytical study using the independent interval approximation.
• Numerical simulations to compare and validate analytical results.
• Analysis of the growth exponent (z) and particle spacing distribution P(k,t).

Main Results:

• A local bias ε alters the universality class of the reaction-diffusion model.
• The growth exponent z changes from 2 (at ε=0) to 1 (for ε>0), indicating a shift to mean-field behavior.
• A new time scale, εt, emerges for non-zero bias values.

Conclusions:

• Local bias is a critical factor that can fundamentally change the macroscopic behavior of reaction-diffusion systems.
• The independent interval approximation effectively captures the scaling behavior observed in simulations.
• The findings provide insights into the role of local perturbations in complex systems.