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Spontaneous symmetry breaking and periodic structure in a multilane system
Rui Jiang1, Mao-Bin Hu, Bin Jia
1School of Engineering Science, University of Science and Technology of China, Hefei 230026, China.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 13, 2007
Summary
The multilane totally asymmetric simple exclusion process (TASEP) exhibits distinct behaviors based on the number of lanes. Even lanes show symmetry-breaking phases, while odd lanes reveal a periodic structure dependent on lane and system size.
Area of Science:
- Statistical Mechanics
- Complex Systems
Background:
- The totally asymmetric simple exclusion process (TASEP) is a fundamental model for studying particle transport in one dimension.
- Understanding multilane TASEP with restricted entry is crucial for modeling complex systems with limited access points.
Purpose of the Study:
- To investigate the impact of the number of lanes (n) on the phase behavior of a multilane TASEP with narrow entrances.
- To analyze the influence of parallel update rules and particle entry/exit dynamics on system configurations.
Main Methods:
- Simulations of the multilane TASEP under parallel update conditions.
- Mathematical analysis including mean-field approximations.
- Comparison of simulation results with theoretical predictions.
Main Results:
- For even n, two phases are observed: high-density-low-density (HD-LD) and asymmetric low-density-low-density (LD-LD).
- For odd n, a periodic structure emerges, with the period scaling with lane number (n) and system size (L).
- At injection rate alpha=1, the seesaw phase seen in n=2 disappears, replaced by HD-LD or symmetric LD phases.
Conclusions:
- The number of lanes significantly alters the emergent phases in multilane TASEP with narrow entrances.
- Mean-field approximations provide good agreement for low removal rates but deviate for higher rates due to neglected correlations.
- The study highlights the importance of lane number and boundary conditions in determining transport properties.
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