## Abstract

Let us consider a two-sided multi-species stochastic particle model with finitely many particles on (Formula presented.), defined as follows. Suppose that each particle is labelled by a positive integer l, and waits a random time exponentially distributed with rate 1. It then chooses the right direction to jump with probability p, or the left direction with probability (Formula presented.). If the particle chooses the right direction, it jumps to the nearest site occupied by a particle (Formula presented.) (with the convention that an empty site is considered as a particle with labelled 0). If the particle chooses the left direction, it jumps to the next site on the left only if that site is either empty or occupied by a particle (Formula presented.), and in the latter case, particles l and (Formula presented.) swap their positions. We show that this model is integrable, and provide the exact formula of the transition probability using the Bethe ansatz.

Original language | English |
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Article number | 1164 |

Journal | Symmetry |

Volume | 16 |

Issue number | 9 |

DOIs | |

Publication status | Published - Sept 2024 |

## Keywords

- ASEP
- Bethe ansatz
- exactly solvable models
- integrability
- PushTASEP
- symmetry
- TASEP

## ASJC Scopus subject areas

- Computer Science (miscellaneous)
- Chemistry (miscellaneous)
- General Mathematics
- Physics and Astronomy (miscellaneous)