Abstract
In the present paper, we study stability of the dynamical system corresponding quantum Markov chain (QMC) associated with the Ising model on Cayley tree of order two. To study certain properties of QMC we reduce our investigation to the study of dynamics of a nonlinear dynamical system. For such a dynamical system it is proved existence of exactly three fixed points and absence of periodic points. Moreover, it is established finiteness and infiniteness of the trajectory of the system.
Original language | English |
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Pages (from-to) | 20-27 |
Number of pages | 8 |
Journal | Australian Journal of Basic and Applied Sciences |
Volume | 5 |
Issue number | 3 |
Publication status | Published - Mar 2011 |
Externally published | Yes |
Keywords
- Cayley tree
- Ising model
- Quantum Markov chain
- Stability of the dynamical system
ASJC Scopus subject areas
- General