Non-homogeneous quantum Markov states and quantum Markov fields

DOI10.1016/S0022-1236(03)00071-5zbMath1031.46074MaRDI QIDQ1395791

Francesco Fidaleo, Luigi Accardi

Publication date: 1 July 2003

Published in: Journal of Functional Analysis (Search for Journal in Brave)

zbMATH Keywords

quantum statistical mechanicsquantum Markov processesone-dimensional spin model

Mathematics Subject Classification ID

Applications of selfadjoint operator algebras to physics (46L60) Quantum equilibrium statistical mechanics (general) (82B10) Noncommutative probability and statistics (46L53) Markov processes (60J99)

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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
• Finitely correlated states on quantum spin chains
• The problem of uniqueness of a Gibbsian random field and the problem of phase transitions
• Conditional expectations in von Neumann algebras
• QUANTUM MARKOV FIELDS
• Strong Convergence of Martingales in von Neumann Algebras
• A Characterization of Pure Finitely Correlated States
• MINIMAL EXPECTATIONS FOR INCLUSIONS WITH ATOMIC CENTRES
• MARKOVIAN KMS-STATES FOR ONE-DIMENSIONAL SPIN CHAINS
• Inductive Limits of Finite Dimensional C ∗ -Algebras
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