On matrix product ansatz for Asymmetric Simple Exclusion Process with open boundary in the singular case

Autor: Bryc, Wlodzimierz, Swieca, Marcin
Rok vydání: 2019
Předmět:
Zdroj: Journal of Statistical Physics, 177 (2019), pp. 252-284
Druh dokumentu: Working Paper
DOI: 10.1007/s10955-019-02367-4
Popis: We study a substitute for the matrix product ansatz for Asymmetric Simple Exclusion Process with open boundary in the ``singular case'' $\alpha\beta=q^N\gamma\delta$, when the standard form of the matrix product ansatz of Derrida, Evans, Hakim and Pasquier does not apply. In our approach, the matrix product ansatz is replaced with a pair of linear functionals on an abstract algebra. One of the functionals, $\varphi_1$, is defined on the entire algebra, and determines stationary probabilities for large systems on $L\geq N+1$ sites. The other functional, $\varphi_0$, is defined only on a finite-dimensional linear subspace of the algebra, and determines stationary probabilities for small systems on $L< N+1$ sites. Functional $\varphi_0$ vanishes on non-constant Askey-Wilson polynomials and in non-singular case becomes an orthogonality functional for the Askey-Wilson polynomials.
Comment: This is expanded version of the paper with additional details. The revised version corrects the sign of epsilon in the proof of Theorem 3, and puts correct denominators in the first formula in Proposition 7
Databáze: arXiv
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