Multispecies TASEP and the tetrahedron equation
Multispecies TASEP and the tetrahedron equation
复制标题
多物种 TASEP 和四面体方程
DOI：
10.1088/1751-8113/49/11/114001
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Okado M.
中科院分区：
文献类型：
--
作者：
Kuniba A.;Maruyama S.;Okado M.
在三维格点模型中引入了一族层间转移矩阵，它可以看作是m× n正方格点上q振子值六顶点模型的配分函数.通过调用四面体方程，我们建立了它们的交换性和混合各种边界条件的双线性关系。在q= 0和m= n时，最终给出了作者最近得到的n种群完全不对称简单排斥过程的定态公式的一个新证明，揭示了矩阵乘积构造中的三维可积性.
We introduce a family of layer to layer transfer matrices in a three-dimensional (3D) lattice model which can be viewed as partition functions of the q-oscillator valued six-vertex model on an m× n square lattice. By invoking the tetrahedron equation we establish their commutativity and bilinear relations mixing various boundary conditions. At q= 0 and m= n, they ultimately yield a new proof of the steady state formula for the n-species totally asymmetric simple exclusion process obtained recently by the authors, revealing the 3D integrability in the matrix product construction.