MARKOV STATES AND CHAINS ON THE CAR ALGEBRA
Luigi AccardiCentro Interdisciplinare Vito Volterra, II Università di Roma "Tor Vergata", Via Columbia 2, 00133 Roma, ItalyFrancesco FidaleoDipartimento di Matematica, II Università di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133 Roma, ItalyFarrukh MukhamedovDepartment of Mechanics and Mathematics, National University of Uzbekistan, Vuzgorodok, 700095, Tashkent, Uzbekistan
ABI
Abstract
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.
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