# 2-species TASEP with open boundaries: Baxterisation, integrability and Matrix ansatz.

When |
Dec 03, 2018
from 04:00 PM to 05:00 PM |
---|---|

Where | Salle Est/Ouest du M7 |

Attendees |
Matthieu Vanicat |

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# Lundi 3 Decembre

## Title: 2-species TASEP with open boundaries: Baxterisation, integrability and Matrix ansatz.

# Matthieu Vanicat (Fakulteta za matematiko in fiziko, Université de Ljubljana, Slovénie)

**Abstract: **We present a 2-species Totally asymmetric exclusion process (TASEP) in which the hopping rates depend on the species of the particle. The lattice is connected at its extremities to particle reservoirs: particles are injected and extracted with given probability rates. The system is driven out-of-equilibrium, there is a non-vanishing particle current in the stationary state.

We show that the model is Yang-Baxter integrable: the Markov matrix -encoding the stochastic dynamics- is constructed from the Sklyanin transfer matrix. The integrable structure has nevertheless some specificities:

-The associated R-matrix depends separately on two spectral parameters and does not seem to be related to any known quantum groups. We show that it can be constructed from a very simple braid-like algebra through a Baxterisation procedure.

-The R-matrix has some singularity which prevents us to prove the commutation relation of the Sklyanin transfer matrix in the usual way. We present an alternative proof.

Finally we provide an exact construction of the stationary state of the model using Matrix ansatz.