Markov states and chains on the car algebra

Luigi Accardi, Francesco Fidaleo, Farruh Mukhamedov

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)


We introduce the notion of Markov states and chains on the Canonical Anticommutation Relations algebra over ℤ, emphasizing some remarkable differences with the infinite tensor product case. We describe the structure of the Markov states on this algebra and show that, contrarily to the infinite tensor product case, not all these states are diagonalizable. A general method to construct nontrivial quantum Markov chains on the CAR algebra is also proposed and illustrated by some pivotal examples. This analysis provides a further step for a satisfactory theory of quantum Markov processes.

Original languageEnglish
Pages (from-to)165-183
Number of pages19
JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
Issue number2
Publication statusPublished - Jun 2007
Externally publishedYes


  • Integration and probability
  • Mathematical quantum statistical mechanics
  • Noncommutative measure
  • Quantum Markov processes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Mathematical Physics
  • Applied Mathematics


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