20.500.12556/RUL-105240
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.
quantum mechanics
matrix ansatz
zero range process
open boundaries
exact results
hidden Markov chains
kvantna mehanika
true
false
false
Angleški jezik
Slovenski jezik
Neznano
2018-11-13 14:50:35
2018-11-13 14:50:35
2022-08-18 03:43:12
0000-00-00 00:00:00
2018
0
0
11 str.
art. no. 245001
Vol. 51
May 2018
0000-00-00
PostprintKoncna
Objavljeno
NiDoloceno
0000-00-00
0000-00-00
0000-00-00
2019-05-21
530.145
1751-8113
10.1088/1751-8121/aac196
3265124
3692314
RAZ_Bertin_Eric_i2018.pdf
RAZ_Bertin_Eric_i2018.pdf
1
22F1D2DC6B81B112656619ED28D8A5A4
425ef9eb902a5d157fbcb170a7a2d2cd6b9cec3e03de7331ac631081dbd50278
2619f661-a1b6-11eb-a523-00155dcfd717
https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=115853
https://iopscience.iop.org/article/10.1088/1751-8121/aac196
1
https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=140325
Fakulteta za matematiko in fiziko
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0
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