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

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...

Full description

Bibliographic Details
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/
http://irep.iium.edu.my/1817/
http://irep.iium.edu.my/1817/
http://irep.iium.edu.my/1817/1/acmfms-AHP%282011%29.pdf
id iium-1817
recordtype eprints
spelling iium-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 PeerReviewed 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
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
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/
http://irep.iium.edu.my/1817/
http://irep.iium.edu.my/1817/
http://irep.iium.edu.my/1817/1/acmfms-AHP%282011%29.pdf
first_indexed 2023-09-18T20:09:20Z
last_indexed 2023-09-18T20:09:20Z
_version_ 1777407372402098176

Similar Items