scholarly journals ON QUANTUM MARKOV CHAINS ON CAYLEY TREE I: UNIQUENESS OF THE ASSOCIATED CHAIN WITH XY-MODEL ON THE CAYLEY TREE OF ORDER TWO

2011 ◽  
Vol 14 (03) ◽  
pp. 443-463 ◽  
Author(s):  
LUIGI ACCARDI ◽  
FARRUKH MUKHAMEDOV ◽  
MANSOOR SABUROV
Keyword(s):  
Markov Chains ◽  
Boundary Conditions ◽  
Cayley Tree ◽  
Weak Limit ◽  
Finite Volumes ◽  
Xy Model ◽  
Quantum Markov Chains

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.

Uniqueness of Quantum Markov Chain Associated with XY-Ising Model on Cayley Tree of Order Two

2017 ◽  
Vol 24 (02) ◽  
pp. 1750010 ◽  
Author(s):  
Farrukh Mukhamedov ◽  
Soueidy El Gheteb
Keyword(s):  
Markov Chain ◽  
Ising Model ◽  
Markov Chains ◽  
Boundary Conditions ◽  
Finite Volume ◽  
Cayley Tree ◽  
Limit State ◽  
Weak Limit ◽  
Quantum Markov Chain ◽  
Quantum Markov Chains

In this paper, we consider backward and forward Quantum Markov Chains (QMC) associated with XY -Ising model on the Cayley tree of order two. We construct finite volume states with boundary conditions, and define QMC as a weak limit of those states which depend on the boundary conditions. We prove that the limit state is a unique QMC associated with such a model, this means the QMC does not depend on the boundary conditions. Moreover, we observe the relation between backward and forward QMC.

scholarly journals Uniqueness of quantum Markov chains associated with an XY-model on a cayley tree of order 2

2011 ◽  
Vol 90 (1-2) ◽  
pp. 162-174 ◽  
Author(s):  
L. Accardi ◽  
F. M. Mukhamedov ◽  
M. Kh. Saburov
Keyword(s):  
Markov Chains ◽  
Cayley Tree ◽  
Xy Model ◽  
Quantum Markov Chains

scholarly journals Phase Transitions for Quantum Markov Chains Associated with Ising Type Models on a Cayley Tree

2016 ◽  
Vol 163 (3) ◽  
pp. 544-567 ◽  
Author(s):  
Farrukh Mukhamedov ◽  
Abdessatar Barhoumi ◽  
Abdessatar Souissi
Keyword(s):  
Phase Transitions ◽  
Markov Chains ◽  
Cayley Tree ◽  
Quantum Markov Chains

scholarly journals On Translation Invariant Quantum Markov Chains associated with Ising-XY models on a Cayley tree

2017 ◽  
Vol 819 ◽  
pp. 012006
Author(s):  
Farrukh Mukhamedov ◽  
Abdessatar Barhoumi ◽  
Abdessatar Souissi ◽  
Soueidy El Gheteb
Keyword(s):  
Markov Chains ◽  
Cayley Tree ◽  
Translation Invariant ◽  
Invariant Quantum ◽  
Quantum Markov Chains

scholarly journals On Quantum Markov Chains on Cayley Tree III: Ising Model

2014 ◽  
Vol 157 (2) ◽  
pp. 303-329 ◽  
Author(s):  
Luigi Accardi ◽  
Farrukh Mukhamedov ◽  
Mansoor Saburov
Keyword(s):  
Ising Model ◽  
Markov Chains ◽  
Cayley Tree ◽  
Quantum Markov Chains

Factors Generated by XY-Model with Competing Ising Interactions on the Cayley Tree

2019 ◽  
Vol 21 (1) ◽  
pp. 241-253 ◽  
Author(s):  
Farrukh Mukhamedov ◽  
Soueidy El Gheteb
Keyword(s):  
Cayley Tree ◽  
Xy Model

scholarly journals On a stochastic Burgers equation with Dirichlet boundary conditions

2003 ◽  
Vol 2003 (43) ◽  
pp. 2735-2746 ◽  
Author(s):  
Ekaterina T. Kolkovska
Keyword(s):  
Weak Solution ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Burgers Equation ◽  
Martingale Problem ◽  
Weak Limit ◽  
Dirichlet Boundary Conditions ◽  
One Dimensional ◽  
Stochastic Burgers Equation ◽  
The One

We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.

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