Generalized matrix Ansatz in the multispecies exclusion process—the partially asymmetric case
Generalized matrix Ansatz in the multispecies exclusion process—the partially asymmetric case
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多物种排除过程中的广义矩阵 Ansatz——部分不对称情况
DOI：
10.1088/1751-8113/45/19/195001
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Sylvain Prolhac
中科院分区：
文献类型：
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作者：
C. Arita;Arvind Ayyer;K. Mallick;Sylvain Prolhac
我们研究了环上不对称简单排除过程的最简单的多物种推广之一。该过程具有丰富的组合谱结构和稳态的矩阵乘积形式。在完全不对称的情况下，作者获得了与不同物种数量的系统动力学共轭的算子，最近由 Arita 等人报道（2011 J. Phys. A: Math. Theor. 44 335004）。这种非平凡算子的存在被重新表述为特定二次代数（广义矩阵 Ansatz）的表示问题。在这项工作中，我们为部分不对称的情况明确构建了表示族。该解不能通过完全不对称情况的简单变形来获得。
We investigate one of the simplest multispecies generalizations of the asymmetric simple exclusion process on a ring. This process has a rich combinatorial spectral structure and a matrix product form for the stationary state. In the totally asymmetric case, operators that conjugate the dynamics of systems with different numbers of species were obtained by the authors and recently reported by Arita et al (2011 J. Phys. A: Math. Theor. 44 335004). The existence of such nontrivial operators was reformulated as a representation problem for a specific quadratic algebra (generalized matrix Ansatz). In this work, we construct the family of representations explicitly for the partially asymmetric case. This solution cannot be obtained by a simple deformation of the totally asymmetric case.