Recursive structures in the multispecies TASEP
Recursive structures in the multispecies TASEP
复制标题
多物种 TASEP 中的递归结构
DOI：
10.1088/1751-8113/44/33/335004
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发表时间：
2011
期刊：
影响因子：
--
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
用简单跳变规则考虑了完全不对称简单不相容过程（TASEP）的多种推广：对于α和βth类粒子（α < β）， αβ→βα的跃迁速率与α和β值无关。法拉利和马丁（2007）。Prob. 35 807)通过组合算法获得了该模型的稳态，随后Evans等人（2009 J. Stat. Phys. 135 217）将其解释为矩阵乘积表示。这种“矩阵分析”表明，N类粒子的多态TASEP （N-TASEP）的定态可以通过算子作用于(N−1)-TASEP定态的代数构造。此外，Arita et al . （2009 J. Phys.）a . Math theory . 45 345002)分析了马尔可夫矩阵的光谱结构：他们表明N-TASEP的特征值集包含(N−1)-TASEP的特征值集，并且各种光谱内含物可以用称为Hasse图的分层集合论结构进行编码。受这些工作的启发，我们定义了非平凡算子，允许我们通过提升(N−1)-TASEP的特征向量来构造N-TASEP的特征向量。这一目标是通过推广矩阵乘积表示和法拉利-马丁算法来实现的。特别地，我们证明了矩阵ansatz不仅是一个写定态的方便工具，而且实际上是不同N值的马尔可夫矩阵的交织。
We consider a multispecies generalization of the totally asymmetric simple exclusion process (TASEP) with the simple hopping rule: for the α and βth-class particles (α < β), the transition αβ → βα occurs with a rate independent from the values α and β. Ferrari and Martin (2007 Ann. Prob. 35 807) obtained the stationary state of this model thanks to a combinatorial algorithm, which was subsequently interpreted as a matrix product representation by Evans et al (2009 J. Stat. Phys. 135 217). This ‘matrix ansatz’ shows that the stationary state of the multispecies TASEP with N classes of particles (N-TASEP) can be constructed algebraically by the action of an operator on the (N − 1)-TASEP stationary state. Besides, Arita et al (2009 J. Phys. A. Math Theor. 45 345002) analyzed the spectral structure of the Markov matrix: they showed that the set of eigenvalues of the N-TASEP contains those of the (N − 1)-TASEP and that the various spectral inclusions can be encoded in a hierarchical set-theoretic structure known as the Hasse diagram. Inspired by these works, we define nontrivial operators that allow us to construct eigenvectors of the N-TASEP by lifting the eigenvectors of the (N − 1)-TASEP. This goal is achieved by generalizing the matrix product representation and the Ferrari–Martin algorithm. In particular, we show that the matrix ansatz is not only a convenient tool to write the stationary state but in fact intertwines Markov matrices of different values of N.
影响因子：
0.4
作者：
Kenji Kajiwara;Masanobu Kaneko;Atsushi Nobe;Teruhisa Tsuda
通讯作者：
Kenji Kajiwara;Masanobu Kaneko;Atsushi Nobe;Teruhisa Tsuda
相互作用的布朗粒子的零温度限制，II._一维凝固。
DOI：
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发表时间：
2004
期刊：
Ann. Probab. 32
影响因子：
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作者：
Hiromitsu Suetani;Takehiko Horita;Shin Mizutani;T.Funaki
通讯作者：
T.Funaki