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Matrix product representation of the stationary state of the open zero range process
ID
Bertin, Eric
(
Author
),
ID
Vanicat, Matthieu
(
Author
)
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https://iopscience.iop.org/article/10.1088/1751-8121/aac196
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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.
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
Views:
1373
Downloads:
636
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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
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