TY - JOUR
T1 - On quantum markov chains on cayley tree i
T2 - Uniqueness of the associated chain with xy-model on the cayley tree of order two
AU - Accardi, Luigi
AU - Mukhamedov, Farrukh
AU - Saburov, Mansoor
N1 - Funding Information:
The present study have been done within the Grant FRGS0308-91 of Malaysian Ministry of Higher Education. A final part of this work was done at the Abdus Salam International Center for Theoretical Physics (ICTP), Trieste, Italy. F.M. thanks the ICTP for providing financial support of his visit (within the scheme of Junior Associate) to ICTP. The authors (F.M., M.S.) also acknowledge the Malaysian Ministry of Science, Technology and Innovation Grant 01-01-08-SF0079.
PY - 2011/9
Y1 - 2011/9
N2 - In this 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 Cayley 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.
AB - In this 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 Cayley 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.
KW - Cayley tree
KW - Quantum Markov chain
KW - XY-model
KW - uniqueness
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U2 - 10.1142/S021902571100447X
DO - 10.1142/S021902571100447X
M3 - Article
AN - SCOPUS:79961030843
SN - 0219-0257
VL - 14
SP - 443
EP - 463
JO - Infinite Dimensional Analysis, Quantum Probability and Related Topics
JF - Infinite Dimensional Analysis, Quantum Probability and Related Topics
IS - 3
ER -