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On quantum Markov chains on Cayley tree II: phase transitions for the associated chain with XY -Model on the Cayley tree of order tree

In the present paper, we study forward quantum Markov chains (QMC) defined on a Cayley tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on a Cayley tree. By means of such constructions we prove the existence of a phase transition for the XY -model on a Cayle...

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Main Authors: Accardi, Luigi, Mukhamedov, Farrukh, Saburov, Mansoor
Format: Article
Language:English
Published: Birkhaeuser Verlag AG 2011
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/1817/1/acmfms-AHP%282011%29.pdf
http://irep.iium.edu.my/1817/
http://link.springer.com/article/10.1007%2Fs00023-011-0107-2
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spelling my.iium.irep.18172014-06-11T03:29:11Z http://irep.iium.edu.my/1817/ On quantum Markov chains on Cayley tree II: phase transitions for the associated chain with XY -Model on the Cayley tree of order tree Accardi, Luigi Mukhamedov, Farrukh Saburov, Mansoor QA Mathematics In the present paper, we study forward quantum Markov chains (QMC) defined on a Cayley tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on a Cayley tree. By means of such constructions we prove the existence of a phase transition for the XY -model on a Cayley tree of order three in QMC scheme. By the phase transition we mean the existence of two distinct QMC for the given family of interaction operators {K_{x,y}}. Birkhaeuser Verlag AG 2011-09 Article REM application/pdf en http://irep.iium.edu.my/1817/1/acmfms-AHP%282011%29.pdf Accardi, Luigi and Mukhamedov, Farrukh and Saburov, Mansoor (2011) On quantum Markov chains on Cayley tree II: phase transitions for the associated chain with XY -Model on the Cayley tree of order tree. Annales Henri Poincare, 12 (6). pp. 1109-1144. ISSN 1424-0637 http://link.springer.com/article/10.1007%2Fs00023-011-0107-2 10.1007/s00023-011-0107-2
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 II: phase transitions for the associated chain with XY -Model on the Cayley tree of order tree
description In the present paper, we study forward quantum Markov chains (QMC) defined on a Cayley tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on a Cayley tree. By means of such constructions we prove the existence of a phase transition for the XY -model on a Cayley tree of order three in QMC scheme. By the phase transition we mean the existence of two distinct QMC for the given family of interaction operators {K_{x,y}}.
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 II: phase transitions for the associated chain with XY -Model on the Cayley tree of order tree
title_short On quantum Markov chains on Cayley tree II: phase transitions for the associated chain with XY -Model on the Cayley tree of order tree
title_full On quantum Markov chains on Cayley tree II: phase transitions for the associated chain with XY -Model on the Cayley tree of order tree
title_fullStr On quantum Markov chains on Cayley tree II: phase transitions for the associated chain with XY -Model on the Cayley tree of order tree
title_full_unstemmed On quantum Markov chains on Cayley tree II: phase transitions for the associated chain with XY -Model on the Cayley tree of order tree
title_sort on quantum markov chains on cayley tree ii: phase transitions for the associated chain with xy -model on the cayley tree of order tree
publisher Birkhaeuser Verlag AG
publishDate 2011
url http://irep.iium.edu.my/1817/1/acmfms-AHP%282011%29.pdf
http://irep.iium.edu.my/1817/
http://link.springer.com/article/10.1007%2Fs00023-011-0107-2
_version_ 1643604868359782400
score 13.209306

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