Eric Bertin (Author), Matthieu Vanicat (Author)

Abstract

Many one-dimensional lattice particle models with open boundaries, like the paradigmatic asymmetric simple exclusion process (ASEP), have their stationary states represented in the form of a matrix product, with matrices that do not explicitly depend on the lattice site. In contrast, the stationary state of the open 1D zero-range process (ZRP) takes an inhomogeneous factorized form, with site-dependent probability weights. We show that in spite of the absence of correlations, the stationary state of the open ZRP can also be represented in a matrix product form, where the matrices are site-independent, non-commuting and determined from algebraic relations resulting from the master equation. We recover the known distribution of the open ZRP in two different ways: first, using an explicit representation of the matrices and boundary vectors; second, from the sole knowledge of the algebraic relations satisfied by these matrices and vectors. Finally, an interpretation of the relation between the matrix product form and the inhomogeneous factorized form is proposed within the framework of hidden Markov chains.

Keywords

kvantna mehanika;quantum mechanics;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 530.145
COBISS: 3265124 Link will open in a new window
ISSN: 1751-8113
Views: 725
Downloads: 419
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Other data

Secondary language: Slovenian
Secondary keywords: kvantna mehanika;
Embargo end date (OpenAIRE): 2019-05-21
Pages: str. 1-11
Volume: ǂVol. ǂ51
Issue: ǂissue ǂ24
Chronology: May 2018
DOI: 10.1088/1751-8121/aac196
ID: 10983611