We investigate the structure of the Markov states on general Fermi 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 Fermionic annihilators and creators on each site), also the nonhomogeneous 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 Zn, 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 quantum information theory as well.

Fidaleo, F. (2011). Fermi-Markov states. JOURNAL OF OPERATOR THEORY, 66(2), 385-414.

Fermi-Markov states

FIDALEO, FRANCESCO
2011

Abstract

We investigate the structure of the Markov states on general Fermi 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 Fermionic annihilators and creators on each site), also the nonhomogeneous 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 Zn, 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 quantum information theory as well.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - Analisi Matematica
eng
Applications of selfadjoint operator algebras to physics; quantum Markov processes; mathematical quantum statistical mechanics
http://www.theta.ro/jot/archive/2011-066-002/2011-066-002-006.html
Fidaleo, F. (2011). Fermi-Markov states. JOURNAL OF OPERATOR THEORY, 66(2), 385-414.
Fidaleo, F
Articolo su rivista
File in questo prodotto:
File Dimensione Formato  
25.pdf

non disponibili

Licenza: Copyright dell'editore
Dimensione 275.89 kB
Formato Adobe PDF
275.89 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/91889
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? ND
social impact