On factors associated with quantum markov states corresponding to nearest neighbor models on a cayley tree

Francesco Fidaleo; Farruh Mukhamedov

doi:10.1142/9789812702104_0016

On factors associated with quantum markov states corresponding to nearest neighbor models on a cayley tree

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

In this paper we consider nearest neighbour models where the spin takes values in the set Φ = {η₁, η₂, . .., η_q} and is assigned to the vertices of the Cayley tree Γ^k. The Hamiltonian is defined by some given λ-function. We find a condition for the function λ to determine the type of the von Neumann algebra generated by the GNS - construction associated with the quantum Markov state corresponding to the unordered phase of the λ-model. Also we give some physical applications of the obtained result.

Original language	English
Title of host publication	Quantum Probability And Infinite Dimensional Analysis
Subtitle of host publication	From Foundations To Appllications
Publisher	World Scientific Publishing Co.
Pages	237-251
Number of pages	15
ISBN (Electronic)	9789812702104
DOIs	https://doi.org/10.1142/9789812702104_0016
Publication status	Published - Jan 1 2005
Externally published	Yes

Keywords

Cayley tree
Construction
GNS
Gibbs measure
Quantum markov state
Unordered phase
Von neumann algebra
λ-model

ASJC Scopus subject areas

General Mathematics
General Physics and Astronomy

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10.1142/9789812702104_0016

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abstract = "In this paper we consider nearest neighbour models where the spin takes values in the set Φ = {η1, η2, . .., ηq} and is assigned to the vertices of the Cayley tree Γk. The Hamiltonian is defined by some given λ-function. We find a condition for the function λ to determine the type of the von Neumann algebra generated by the GNS - construction associated with the quantum Markov state corresponding to the unordered phase of the λ-model. Also we give some physical applications of the obtained result.",

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author = "Francesco Fidaleo and Farruh Mukhamedov",

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year = "2005",

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doi = "10.1142/9789812702104_0016",

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T1 - On factors associated with quantum markov states corresponding to nearest neighbor models on a cayley tree

AU - Fidaleo, Francesco

AU - Mukhamedov, Farruh

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N2 - In this paper we consider nearest neighbour models where the spin takes values in the set Φ = {η1, η2, . .., ηq} and is assigned to the vertices of the Cayley tree Γk. The Hamiltonian is defined by some given λ-function. We find a condition for the function λ to determine the type of the von Neumann algebra generated by the GNS - construction associated with the quantum Markov state corresponding to the unordered phase of the λ-model. Also we give some physical applications of the obtained result.

AB - In this paper we consider nearest neighbour models where the spin takes values in the set Φ = {η1, η2, . .., ηq} and is assigned to the vertices of the Cayley tree Γk. The Hamiltonian is defined by some given λ-function. We find a condition for the function λ to determine the type of the von Neumann algebra generated by the GNS - construction associated with the quantum Markov state corresponding to the unordered phase of the λ-model. Also we give some physical applications of the obtained result.

KW - Cayley tree

KW - Construction

KW - GNS

KW - Gibbs measure

KW - Quantum markov state

KW - Unordered phase

KW - Von neumann algebra

KW - λ-model

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EP - 251

BT - Quantum Probability And Infinite Dimensional Analysis

PB - World Scientific Publishing Co.

ER -

On factors associated with quantum markov states corresponding to nearest neighbor models on a cayley tree

Abstract

Keywords

ASJC Scopus subject areas

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