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Matrix-product ansatz for the totally asymmetric simple exclusion process with a generalized update on a ring
B L Aneva1, J G Brankov2,3
1Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria.
Physical Review. E
|September 15, 2016
Summary
We derived the finite-size pair correlation function for a generalized exclusion process using matrix-product methods. This reveals particle attraction/repulsion dynamics and aggregation behavior in different regimes.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Non-equilibrium Systems
Background:
- The totally asymmetric simple exclusion process (TASEP) is a fundamental model for studying particle transport in various systems.
- Understanding particle interactions and correlations is crucial for predicting system behavior, especially in non-equilibrium conditions.
- Existing models often simplify dynamics; generalized models are needed for broader applicability.
Purpose of the Study:
- To investigate a generalized discrete-time TASEP on a ring with two hopping probabilities, p and p̃.
- To derive exact finite-size expressions for key statistical quantities, including the pair correlation function.
- To analyze particle interaction regimes (attraction/repulsion) and aggregation phenomena.
Main Methods:
- Application of the matrix-product ansatz.
- Construction of a quadratic algebra and its two-dimensional matrix-product representation.
- Derivation of exact analytical expressions for the partition function, particle current, and correlation functions.
Main Results:
- Exact finite-size expressions for the partition function, particle current, and two-point correlation function were obtained.
- The finite-size pair correlation function was derived for the first time.
- Particle behavior was analyzed in regimes of effective attraction (p̃ > p) and repulsion (p̃ < p).
Conclusions:
- The derived pair correlation function provides new insights into particle interactions in generalized TASEP models.
- An analytic expression for the pair correlation function in the irreversible aggregation limit (p̃ → 1) was obtained.
- The study offers a powerful framework for analyzing complex particle dynamics in discrete-time exclusion processes.
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