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Exclusion process on two intersecting lanes with constrained resources: Symmetry breaking and shock dynamics
Akriti Jindal1, Arvind Kumar Gupta1
1Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140001, Punjab, India.
Physical Review. E
|August 20, 2021
Summary
This study investigates particle exclusion on a two-lane network. Symmetry breaking occurs with increasing particle numbers, leading to asymmetric phases and persistent shocks, explained by domain-wall theory.
Area of Science:
- Statistical Mechanics
- Complex Networks
- Theoretical Physics
Background:
- The exclusion process is a fundamental model in statistical mechanics.
- Understanding particle dynamics on complex network topologies is crucial.
- Investigating systems with competing particle flows reveals emergent behaviors.
Purpose of the Study:
- To analyze the exclusion process on a unique two-intersecting-lane network topology.
- To derive analytical solutions for stationary properties using theoretical frameworks.
- To explore symmetry breaking and shock phenomena under varying particle densities.
Main Methods:
- Mean-field approximation for theoretical analysis.
- Domain-wall theory to explain system dynamics.
- Extensive Monte Carlo simulations for validation.
Main Results:
- Analytical derivation of phase transitions, density profiles, and domain wall positions.
- Observed symmetry breaking beyond a critical particle number, leading to asymmetric phases.
- Identification of bulk-induced shocks in symmetric phases and boundary-induced shocks in both symmetric and asymmetric phases.
Conclusions:
- The system exhibits complex phase diagram behavior with non-monotonic complexity.
- Symmetry breaking is a persistent feature, even at infinite particle numbers.
- Shocks play a key role in understanding phase transitions in this network model.
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