Matrix product representation of the stationary state of the open zero range process
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.
2018
2018-11-13 14:50:35
1033
kvantna mehanika
Eric
Bertin
70
Matthieu
Vanicat
70
UDK
4
530.145
ISSN pri Ä¨lanku
9
1751-8113
DOI
15
10.1088/1751-8121/aac196
COBISS_ID
3
3265124
OceCobissID
13
3692314
RAZ_Bertin_Eric_i2018.pdf
223627
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2018-11-13 14:54:25
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Izvorni URL
2021-02-12 14:37:34