Integrable multi-species SSEP with reactive particle species

Abstract

We investigate integrable exclusion Markov processes constructed from set-theoretical solutions of the Yang-Baxter Equation (YBE) that generalise the multi-species Symmetric Simple Exclusion Process (SSEP). We first introduce the process called the $ (p,1) $-SSEP that is analogous to the multi-species SSEP but with an extra particle species qualified as reactive. Reactive species are able to evaporate and condensate by pairs or to transform by pairs depending on the interpretation. We provide a full combinatorial study of the sectors in the periodic case. We prove the integrability of the process in the periodic case and in the open case for two types of boundaries that we introduce using Baxterisations of solutions of the reflection equation. Next we move on to the process called $ (p,q) $-SSEP, i.e. the multi-species SSEP with an arbitrary number of reactive particle species. We prove its integrability in the periodic case and, for the open case, we introduce integrable boundaries generalising the ones considered for the $ (p,1) $-SSEP. Finally, we define physical quantities relevant to the models and we compute them in the non-equilibrium stationary state of the open $ (p,q) $-SSEP for one type of integrable boundaries.