AI 中文总结
研究由杨-巴克斯特方程解构建的可积多物种SSEP，引入含反应性粒子种类的$(p,1)$-SSEP和$(p,q)$-SSEP，证明其周期及开放情形的可积性，定义并计算了相关物理量。
AI 中文摘要
我们研究了由杨-巴克斯特方程（YBE）的集合论解构建的可积排斥马尔可夫过程，它推广了多物种对称简单排斥过程（SSEP）。首先引入了$(p,1)$-SSEP，它类似于多物种SSEP，但有额外的反应性粒子种类，能成对蒸发、凝聚或转化。对周期情形的扇区进行了完整组合研究，证明了周期情形及开放情形下两种边界类型的可积性。接着研究了$(p,q)$-SSEP，证明了其周期情形的可积性，为开放情形引入了可积边界。最后定义了相关物理量并在开放$(p,q)$-SSEP的一种可积边界的非平衡稳态下进行了计算。
英文摘要
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.
Comments34 pages, 7 figures
