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Matrix product representation of the stationary state of the open zero range process
Bertin, Eric (Avtor), Vanicat, Matthieu (Avtor)

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Izvleček
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.

Jezik:Angleški jezik
Ključne besede:quantum mechanics, matrix ansatz, zero range process, open boundaries, exact results, hidden Markov chains
Tipologija:1.01 - Izvirni znanstveni članek
Organizacija:FMF - Fakulteta za matematiko in fiziko
Leto izida:2018
Št. strani:11 str.
Številčenje:Vol. 51, art. no. 245001
UDK:530.145
ISSN pri članku:1751-8113
DOI:10.1088/1751-8121/aac196 Povezava se odpre v novem oknu
COBISS.SI-ID:3265124 Povezava se odpre v novem oknu
Število ogledov:379
Število prenosov:184
Metapodatki:XML RDF-CHPDL DC-XML DC-RDF
 
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Gradivo je del revije

Naslov:Journal of physics
Skrajšan naslov:J. phys., A, Math. theor.
Založnik:IOP Publishing
ISSN:1751-8113
COBISS.SI-ID:3692314 Povezava se odpre v novem oknu

Gradivo je financirano iz projekta

Financer:EC - European Commission
Program financ.:H2020
Številka projekta:694544
Naslov:Open many-body non-equilibrium systems
Akronim:OMNES

Sekundarni jezik

Jezik:Slovenski jezik
Ključne besede:kvantna mehanika

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