On the integrability of zero-range chipping models with factorized steady states
On the integrability of zero-range chipping models with factorized steady states
复制标题
具有因式分解稳态的零范围碎裂模型的可积性
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
A. Povolotsky
中科院分区：
文献类型：
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作者：
A. Povolotsky
检查了 Evans 等人 (2004 J. Phys. A: Math. Gen. 37 L275) 中提出的具有因式分解稳态的一般零范围碎裂模型的可积性条件。我们找到了 Bethe ansatz 可解的模型的三参数跳跃概率族，其中包括大多数已知的可积随机粒子模型作为极限情况。该解决方案基于遵守一般齐次二次关系的关联代数的两个元素的量子二项式公式，该公式作为副产品得到了证明。我们使用 Bethe ansatz 来解决马尔可夫过程的转移矩阵的特征问题。在此基础上，我们猜想了无限格子上模型演化算子格林函数的积分公式，并推导了环上模型谱的Bethe方程。
The conditions of the integrability of general zero range chipping models with factorized steady states, which were proposed in Evans et al (2004 J. Phys. A: Math. Gen. 37 L275), are examined. We find a three-parametric family of hopping probabilities for the models solvable by the Bethe ansatz, which includes most of known integrable stochastic particle models as limiting cases. The solution is based on the quantum binomial formula for two elements of an associative algebra obeying generic homogeneous quadratic relations, which is proved as a byproduct. We use the Bethe ansatz to solve an eigenproblem for the transition matrix of the Markov process. On its basis, we conjecture an integral formula for the Green function of the evolution operator for the model on an infinite lattice and derive the Bethe equations for the spectrum of the model on a ring.
影响因子：
3
作者：
Borodin, Alexei;Corwin, Ivan;Ferrari, Patrik
通讯作者：
Ferrari, Patrik