N-species stochastic models with boundaries and quadratic algebras
N-species stochastic models with boundaries and quadratic algebras
复制标题
具有边界和二次代数的 N 种随机模型
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
V. Rittenberg
中科院分区：
文献类型：
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作者：
F. C. Alcaraz;S. Dasmahapatra;V. Rittenberg
利用矩阵乘积分析方法，得到了两端为闭端或开端的线性链上随机过程的平稳概率分布。矩阵是一些二次代数的表示。所考虑的代数和表示类型取决于边界条件。在量子链的语言中，我们得到了具有自由边界条件或一端或两端具有非对角边界项的n态量子链的基态。与涉及Bethe ansatz的问题相反，我们没有任意N的一般框架，当特殊化时，给出N = 2的已知结果；事实上，N = 2和N = 2的情况看起来非常不同。
Stationary probability distributions for stochastic processes on linear chains with closed or open ends are obtained using the matrix product ansatz. The matrices are representations of some quadratic algebras. The algebras and the types of representations considered depend on the boundary conditions. In the language of quantum chains we obtain the ground state of N-state quantum chains with free boundary conditions or with non-diagonal boundary terms at one or both ends. In contrast to problems involving the Bethe ansatz, we do not have a general framework for arbitrary N, which when specialized, gives the known results for N = 2; in fact, the N = 2 and N>2 cases appear to be very different.