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arXiv 1403.6963math-phcond-mat.stat-mechmath.MP
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开ASEP的Bethe算子和Q算子

Bethe Ansatz and Q-operator for the open ASEP

Alexandre Lazarescu, Vincent Pasquier

摘要:

在本文中,我们研究了具有开边界的非对称简单排斥过程的电流计数变形。我们构造了一个双参数的家庭的转移矩阵,可交换的变形马尔可夫矩阵的系统。我们表明,这些转移矩阵可以分解成两个交换矩阵,每个参数,这可以确定与巴克斯特的Q-算子,并为这些参数的产品的某些值,他们分解成两个交换矩阵的总和,其中之一是贝特转移矩阵的辅助空间的一个给定的维度。利用这一点,我们找到了开放的ASEP的T-Q方程,并通过功能的Bethe Answer技术,我们得到了变形的马尔可夫矩阵的优势特征值的精确表达式。

英文摘要:

In this paper, we look at the asymmetric simple exclusion process with open boundaries with a current-counting deformation. We construct a two-parameter family of transfer matrices which commute with the deformed Markov matrix of the system. We show that these transfer matrices can be factorised into two commuting matrices with one parameter each, which can be identified with Baxter's Q-operator, and that for certain values of the product of those parameters, they decompose into a sum of two commuting matrices, one of which is the Bethe transfer matrix for a given dimension of the auxiliary space. Using this, we find the T-Q equation for the open ASEP, and, through functional Bethe Ansatz techniques, we obtain an exact expression for the dominant eigenvalue of the deformed Markov matrix.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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