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Stochastic R matrix for Uq(An(¹))

Kuniba, A.; Mangazeev, V.V.; Maruyama, S.; Okado, M.

Description

We show that the quantum R matrix for symmetric tensor representations of Uq(An(¹)) satisfies the sum rule required for its stochastic interpretation under a suitable gauge. Its matrix elements at a special point of the spectral parameter are found to factorize into the form that naturally extends Povolotsky's local transition rate in the q -Hahn process for n=1 . Based on these results we formulate new discrete and continuous time integrable Markov processes on a one-dimensional chain in terms...[Show more]

dc.contributor.authorKuniba, A.
dc.contributor.authorMangazeev, V.V.
dc.contributor.authorMaruyama, S.
dc.contributor.authorOkado, M.
dc.date.accessioned2016-11-08T03:12:11Z
dc.date.available2016-11-08T03:12:11Z
dc.identifier17310
dc.identifier.issn0550-3213
dc.identifier.urihttp://hdl.handle.net/1885/110178
dc.description.abstractWe show that the quantum R matrix for symmetric tensor representations of Uq(An(¹)) satisfies the sum rule required for its stochastic interpretation under a suitable gauge. Its matrix elements at a special point of the spectral parameter are found to factorize into the form that naturally extends Povolotsky's local transition rate in the q -Hahn process for n=1 . Based on these results we formulate new discrete and continuous time integrable Markov processes on a one-dimensional chain in terms of n species of particles obeying asymmetric stochastic dynamics. Bethe ansatz eigenvalues of the Markov matrices are also given.
dc.publisherElsevier
dc.rights© 2016 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/
dc.sourceNuclear Physics B
dc.source.urihttp://repo.scoap3.org/record/17310/files/main.pdf
dc.titleStochastic R matrix for Uq(An(¹))
dc.typeJournal article
dc.date.issued2016-11-04
local.identifier.ariespublicationa383154xPUB4373
local.publisher.urlhttp://www.elsevier.com/
local.type.statusPublished Version
local.contributor.affiliationKuniba, A., Institute of Physics, University of Tokyo, Komaba, Tokyo, 153-8902, Japan
local.contributor.affiliationMangazeev, V.V., Department of Theoretical Physics, Research School of Physics and Engineering, Australian National University, ACT, Canberra, 0200, Australia
local.contributor.affiliationMaruyama, S., Institute of Physics, University of Tokyo, Komaba, Tokyo, 153-8902, Japan
local.contributor.affiliationOkado, M., Department of Mathematics, Osaka City University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan
local.bibliographicCitation.startpage248
local.bibliographicCitation.lastpage277
local.identifier.doi10.1016/j.nuclphysb.2016.09.016
dc.date.updated2016-11-07T03:12:09Z
dcterms.accessRightsOpen Access
CollectionsANU Research Publications

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