Mathematics – Operator Algebras
Scientific paper
2005-06-08
Mathematics
Operator Algebras
32 pages. Journal of Operator Theory, to appear
Scientific paper
We investigate the structure of the Markov states on general Fermion algebras. The situation treated in the present paper covers, beyond the d--Markov states on the CAR algebra on Z (i.e. when there are d--annihilators and creators on each site), also the non homogeneous case (i.e. when the numbers of generators depends on the localization). The present analysis provides the first necessary step for the study of the general properties, and the construction of nontrivial examples of Fermi Markov states on the d--standard lattice, that is the Fermi Markov fields. Natural connections with the KMS boundary condition and entropy of Fermi Markov states are studied in detail. Apart from a class of Markov states quite similar to those arising in the tensor product algebras (called "strongly even" in the sequel), other interesting examples of Fermi Markov states naturally appear. Contrarily to the strongly even examples, the latter are highly entangled and it is expected that they describe interactions which are not "commuting nearest neighbor". Therefore, the non strongly even Markov states, in addition to the natural applications to quantum statistical mechanics, might be of interest for the information theory as well.
No associations
LandOfFree
Fermi Markov states does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Fermi Markov states, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fermi Markov states will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-538717