QUANTUM MARKOV FIELDS

DOI10.1142/S0219025703001079zbMath1052.46047OpenAlexW2149633393MaRDI QIDQ3043494

Francesco Fidaleo, Luigi Accardi

Publication date: 6 August 2004

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219025703001079

zbMATH Keywords

quantum Markov chainnoncommutative measurequantum Markov processesintegration and probabilitymathematical quantum statistical mechanicsUmegaki conditional expectation

Mathematics Subject Classification ID

Discrete-time Markov processes on general state spaces (60J05) Applications of selfadjoint operator algebras to physics (46L60) Quantum equilibrium statistical mechanics (general) (82B10) Noncommutative probability and statistics (46L53) Quantum stochastic calculus (81S25) Operator algebra methods applied to problems in quantum theory (81R15) Markov processes (60J99)

Related Items (19)

Phase transitions for quantum Markov chains associated with Ising type models on a Cayley tree ⋮ MARKOV STATES AND CHAINS ON THE CAR ALGEBRA ⋮ On an algebraic property of the disordered phase of the Ising model with competing interactions on a Cayley tree ⋮ Diagonalizability of quantum Markov states on trees ⋮ Non-homogeneous quantum Markov states and quantum Markov fields ⋮ On quantum Markov chains on Cayley tree. II: Phase transitions for the associated chain with \(XY\)-model on the Cayley tree of order three ⋮ FREE ENERGY DENSITY FOR MEAN FIELD PERTURBATION OF STATES OF A ONE-DIMENSIONAL SPIN CHAIN ⋮ On quantum Markov chains on Cayley tree. III: Ising model ⋮ A quantum Markov chain approach to phase transitions for quantum Ising model with competing XY-interactions on a Cayley tree ⋮ Quantum Markov states on Cayley trees ⋮ Phase transitions for \(XY\)-model on the Cayley tree of order three in quantum Markov chain scheme ⋮ QUANTUM MARKOV FIELDS ON GRAPHS ⋮ Entangled Markov chains ⋮ Factors generated by \textit{XY}-model with competing Ising interactions on the Cayley tree ⋮ ON QUANTUM MARKOV CHAINS ON CAYLEY TREE I: UNIQUENESS OF THE ASSOCIATED CHAIN WITH XY-MODEL ON THE CAYLEY TREE OF ORDER TWO ⋮ Uniqueness of quantum Markov chains associated with an \(XY\)-model on a Cayley tree of order 2 ⋮ Quantum Markov chains associated with Open Quantum random walks ⋮ A Class of Quantum Markov Fields on Tree-like Graphs: Ising-type Model on a Husimi Tree ⋮ Block Markov chains on trees

Cites Work

• Gibbsian random fields for lattice systems with pairwise interactions.
• Local perturbations of conditional expectations
• Conditional expectations in von Neumann algebras and a theorem of Takesaki
• A non-commutative individual ergodic theorem
• Ergodic theory and virtual groups
• The problem of uniqueness of a Gibbsian random field and the problem of phase transitions
• Virtual groups and group actions
• Conditional expectations in von Neumann algebras
• Quasi-Uniform Ergodic Theorems in von Neumann Algebras
• MINIMAL EXPECTATIONS FOR INCLUSIONS WITH ATOMIC CENTRES
• MARKOVIAN KMS-STATES FOR ONE-DIMENSIONAL SPIN CHAINS

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