AI 中文总结
该研究引入与边界储库接触的一维链上的多物种调和过程，推导其R矩阵和K矩阵并构造双行转移矩阵，还定义了三个对偶模型。
AI 中文摘要
我们引入了与边界储库接触的一维链上的调和过程的多物种版本。该过程是一个连续时间马尔可夫链，其中每个位点可容纳无限数量的有色粒子。对称体动力学与储库接触，储库注入和移除粒子，使系统脱离平衡。该过程的马尔可夫生成元与高阶开有理海森堡自旋链的可积哈密顿量一致。我们推导了算子形式的基础R矩阵和K矩阵，并遵循Sklyanin构造了双行转移矩阵。与单物种情况类似，R矩阵可分解为两个R算子，每个因子对应左行和右行粒子。我们进一步定义了三个对偶模型：吸收粒子模型、隐参数模型和热传导模型。
英文摘要
We introduce the multispecies version of the harmonic process on a one-dimensional chain in contact with boundary reservoirs. This process is a continuous-time Markov chain where each site can host an unbounded number of colored particles. The symmetric bulk dynamics is put in contact with reservoirs, which inject and remove particles driving the system out-of-equilibrium. The Markov generator of the process is identified with the integrable Hamiltonian of an open rational Heisenberg spin chain of higher rank. We derive the underlying R- and K-matrices in operator form and construct the double-row transfer matrix following Sklyanin. Similar to the monospecies case the R-matrix factorises into two R-operators, each factor corresponding to left and right moving particles. We further define three dual models: an absorbing particle model, a hidden parameter model and a heat conduction model.
Comments62 pages
