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On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two

In the present paper we study forward Quantum Markov Chains (QMC) defined on Cayley tree. A construction of such QMC is provided, namely we construct states on finite volumes with boundary conditions, and define QMC as a weak limit of those states which depends on the boundary conditions. Using the...

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Main Authors: Accardi, Luigi, Mukhamedov, Farrukh, Saburov, Mansoor
Format: Article
Language:English
Published: World Scientific Publishing 2011
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/6519/1/acmfms-idaqp%282011%29.pdf
http://irep.iium.edu.my/6519/
http://www.worldscinet.com/idaqp/14/preserved-docs/1403/S021902571100447X.pdf
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spelling my.iium.irep.65192014-06-16T04:21:16Z http://irep.iium.edu.my/6519/ On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two Accardi, Luigi Mukhamedov, Farrukh Saburov, Mansoor QA Mathematics In the present paper we study forward Quantum Markov Chains (QMC) defined on Cayley tree. A construction of such QMC is provided, namely we construct states on finite volumes with boundary conditions, and define QMC as a weak limit of those states which depends on the boundary conditions. Using the provided construction we investigate QMC associated with XY-model on a Caylay tree of order two. We prove uniqueness of QMC associated with such a model, this means the QMC does not depend on the boundary conditions of QMC associated with such a model, this means the QMC does not depend on the boundary conditions. World Scientific Publishing 2011-09 Article REM application/pdf en http://irep.iium.edu.my/6519/1/acmfms-idaqp%282011%29.pdf Accardi, Luigi and Mukhamedov, Farrukh and Saburov, Mansoor (2011) On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 14 (3). pp. 443-463. ISSN 0219-0257 http://www.worldscinet.com/idaqp/14/preserved-docs/1403/S021902571100447X.pdf 10.1142/S021902571100447X
institution Universiti Islam Antarabangsa Malaysia
building IIUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider International Islamic University Malaysia
content_source IIUM Repository (IREP)
url_provider http://irep.iium.edu.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Accardi, Luigi
Mukhamedov, Farrukh
Saburov, Mansoor
On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two
description In the present paper we study forward Quantum Markov Chains (QMC) defined on Cayley tree. A construction of such QMC is provided, namely we construct states on finite volumes with boundary conditions, and define QMC as a weak limit of those states which depends on the boundary conditions. Using the provided construction we investigate QMC associated with XY-model on a Caylay tree of order two. We prove uniqueness of QMC associated with such a model, this means the QMC does not depend on the boundary conditions of QMC associated with such a model, this means the QMC does not depend on the boundary conditions.
format Article
author Accardi, Luigi
Mukhamedov, Farrukh
Saburov, Mansoor
author_facet Accardi, Luigi
Mukhamedov, Farrukh
Saburov, Mansoor
author_sort Accardi, Luigi
title On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two
title_short On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two
title_full On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two
title_fullStr On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two
title_full_unstemmed On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two
title_sort on quantum markov chains on cayley tree i: uniqueness of the associated chain with xy-model on the cayley tree of order two
publisher World Scientific Publishing
publishDate 2011
url http://irep.iium.edu.my/6519/1/acmfms-idaqp%282011%29.pdf
http://irep.iium.edu.my/6519/
http://www.worldscinet.com/idaqp/14/preserved-docs/1403/S021902571100447X.pdf
_version_ 1643605750601220096
score 13.159267

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