Matrix product representation of the stationary state of the open zero range process

Bertin, Eric (author), Vanicat, Matthieu (author)

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.

• Language: English
• Keywords: quantum mechanics, matrix ansatz, zero range process, open boundaries, exact results, hidden Markov chains
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2018
• Number of pages: 11 str.
• Numbering: Vol. 51, art. no. 245001
• PID: 20.500.12556/RUL-105240
• UDC: 530.145
• ISSN on article: 1751-8113
• DOI: 10.1088/1751-8121/aac196
• COBISS.SI-ID: 3265124
• Publication date in RUL: 13.11.2018

Record is a part of a journal

• Title: Journal of physics : Mathematical and theoretical
• Shortened title: J. phys., A, Math. theor.
• Publisher: IOP Publishing
• ISSN: 1751-8113
• COBISS.SI-ID: 3692314

Secondary language

• Language: Slovenian
• Keywords: kvantna mehanika

Projects

• Funder: EC - European Commission
• Funding programme: H2020
• Project number: 694544
• Name: Open many-body non-equilibrium systems
• Acronym: OMNES