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

Bertin, Eric (avtor), Vanicat, Matthieu (avtor)

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
• Status publikacije: Objavljeno
• Različica publikacije: Recenzirani rokopis
• Leto izida: 2018
• Št. strani: 11 str.
• Številčenje: Vol. 51, art. no. 245001
• PID: 20.500.12556/RUL-105240
• UDK: 530.145
• ISSN pri članku: 1751-8113
• DOI: 10.1088/1751-8121/aac196
• COBISS.SI-ID: 3265124
• Datum objave v RUL: 13.11.2018

Gradivo je del revije

• Naslov: Journal of physics : Mathematical and theoretical
• Skrajšan naslov: J. phys., A, Math. theor.
• Založnik: IOP Publishing
• ISSN: 1751-8113
• COBISS.SI-ID: 3692314

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: kvantna mehanika

Projekti

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