In this paper we study forward quantum Markov chains (QMC) defined on Cayley tree. A construction of such QMC is provided, namely we construct states on finite volumes with boundary conditions, and define QMC as a weak limit of those states which depends on the boundary conditions. Using the provided construction, we investigate QMC associated with XY-model on a Cayley tree of order two. We prove uniqueness of QMC associated with such a model, this means the QMC does not depend on the boundary conditions.
Accardi, L., Mukhamedov, F., Saburov, M. (2011). On quantum Markov chains on Cayley tree and associated chains with $XY$-model, infinite dimensional analysis, quantum probability and related topics. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 14(3), 443-463 [10.1142/S021902571100447X].
On quantum Markov chains on Cayley tree and associated chains with $XY$-model, infinite dimensional analysis, quantum probability and related topics
ACCARDI, LUIGI;
2011-09-01
Abstract
In this paper we study forward quantum Markov chains (QMC) defined on Cayley tree. A construction of such QMC is provided, namely we construct states on finite volumes with boundary conditions, and define QMC as a weak limit of those states which depends on the boundary conditions. Using the provided construction, we investigate QMC associated with XY-model on a Cayley tree of order two. We prove uniqueness of QMC associated with such a model, this means the QMC does not depend on the boundary conditions.| File | Dimensione | Formato | |
|---|---|---|---|
|
AcMuSa2011.pdf
accesso aperto
Dimensione
312.93 kB
Formato
Adobe PDF
|
312.93 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
