Uniqueness of quantum Markov chains associated with an XY -model on a Cayley tree of order 2

Uniqueness of quantum Markov chains associated with an XY -model on a Cayley tree of order 2

We propose the construction of a quantum Markov chain that corresponds to a “forward” quantum Markov chain. In the given construction, the quantum Markov chain is defined as the limit of finite-dimensional states depending on the boundary conditions. A similar construction is widely used in the def...

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Main Authors: Accardi, Luigi, Mukhamedov, Farrukh, Saburov, Mansoor
Format: Article
Language:English
Published: Pleiades Publishing 2011
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/1614/
http://irep.iium.edu.my/1614/
http://irep.iium.edu.my/1614/
http://irep.iium.edu.my/1614/1/acmfsm-MatNotes%282011%29.pdf
id iium-1614
recordtype eprints
spelling iium-16142013-06-28T01:24:14Z http://irep.iium.edu.my/1614/ Uniqueness of quantum Markov chains associated with an XY -model on a Cayley tree of order 2 Accardi, Luigi Mukhamedov, Farrukh Saburov, Mansoor QA Mathematics We propose the construction of a quantum Markov chain that corresponds to a “forward” quantum Markov chain. In the given construction, the quantum Markov chain is defined as the limit of finite-dimensional states depending on the boundary conditions. A similar construction is widely used in the definition of Gibbs states in classical statistical mechanics. Using this construction, we study the quantum Markov chain associated with an XY -model on a Cayley tree. For this model, within the framework of the given construction, we prove the uniqueness of the quantum Markov chain i.e., we show that the state is independent of the boundary conditions. Pleiades Publishing 2011-02-17 Article PeerReviewed application/pdf en http://irep.iium.edu.my/1614/1/acmfsm-MatNotes%282011%29.pdf Accardi, Luigi and Mukhamedov, Farrukh and Saburov, Mansoor (2011) Uniqueness of quantum Markov chains associated with an XY -model on a Cayley tree of order 2. Mathematical Notes, 90 (2). pp. 8-20. ISSN 0001-4346 http://www.springerlink.com/content/0001-4346 10.1134/S0001434611070029
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
Uniqueness of quantum Markov chains associated with an XY -model on a Cayley tree of order 2
description We propose the construction of a quantum Markov chain that corresponds to a “forward” quantum Markov chain. In the given construction, the quantum Markov chain is defined as the limit of finite-dimensional states depending on the boundary conditions. A similar construction is widely used in the definition of Gibbs states in classical statistical mechanics. Using this construction, we study the quantum Markov chain associated with an XY -model on a Cayley tree. For this model, within the framework of the given construction, we prove the uniqueness of the quantum Markov chain i.e., we show that the state is independent of 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 Uniqueness of quantum Markov chains associated with an XY -model on a Cayley tree of order 2
title_short Uniqueness of quantum Markov chains associated with an XY -model on a Cayley tree of order 2
title_full Uniqueness of quantum Markov chains associated with an XY -model on a Cayley tree of order 2
title_fullStr Uniqueness of quantum Markov chains associated with an XY -model on a Cayley tree of order 2
title_full_unstemmed Uniqueness of quantum Markov chains associated with an XY -model on a Cayley tree of order 2
title_sort uniqueness of quantum markov chains associated with an xy -model on a cayley tree of order 2
publisher Pleiades Publishing
publishDate 2011
url http://irep.iium.edu.my/1614/
http://irep.iium.edu.my/1614/
http://irep.iium.edu.my/1614/
http://irep.iium.edu.my/1614/1/acmfsm-MatNotes%282011%29.pdf
first_indexed 2023-09-18T20:09:01Z
last_indexed 2023-09-18T20:09:01Z
_version_ 1777407352156192768

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