Construction of a matrix product stationary state from solutions of finite size system

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dc.creatorHieida, Yasuhiro
dc.creatorSasamoto, Tomohiro
dc.date2004-03-09
dc.date2004-09-03
dc.date.accessioned2026-07-07T02:56:51Z
dc.date.available2026-07-07T02:56:51Z
dc.descriptionStationary states of stochastic models, which have $N$ states per site, in matrix product form are considered. First we give a necessary condition for the existence of a finite $M$-dimensional matrix product state for any ${N,M}$. Second, we give a method to construct the matrices from the stationary states of small size system when the above condition and $N\le M$ are satisfied. Third, the method by which one can check that the obtained matrices are valid for any system size is presented for the case where $M=N$ is satisfied. The application of our methods is explained using three examples: the asymmetric exclusion process, a model studied in [F. H. Jafarpour: J. Phys. A: Math. Gen. 36 (2003) 7497] and a hybrid of both of the models.
dc.description22 pages, no figure. Major changes: sec.3 was shortened; the list of references were changed. This is the final version, which will appear in J.Phys.A
dc.identifierhttps://arxiv.org/abs/cond-mat/0403235
dc.identifierhttp://arxiv.org/abs/cond-mat/0403235
dc.identifierJ. Phys. A: Math. Gen. 37 (2004) 9873-9889
dc.identifierdoi:10.1088/0305-4470/37/42/003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/23489
dc.subjectStatistical Mechanics
dc.titleConstruction of a matrix product stationary state from solutions of finite size system
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