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- Centre National de la Recherche ScientifiqueFR29 papers
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6 papers · 1 filter
Open Quantum Random Walks and Quantum Markov chains on Trees I: Phase transitions
Farrukh Mukhamedov, Abdessatar Souissi, Tarek Hamdi
In the present paper, we construct QMC (Quantum Markov Chains) associated with Open Quantum Random Walks such that the transition operator of the chain is defined by OQRW and the r…
Quantum Markov Chains on the Comb graphs: Ising model
Farrukh Mukhamedov, Abdessatar Souissi, Tarek Hamdi
In the present paper, we construct quantum Markov chains (QMC) over the Comb graphs. As an application of this construction, it is proved the existence of the disordered phase for…
Refinement of quantum Markov states on trees
Farrukh Mukhamedov, Abdessatar Souissi
In the present paper, we propose a refinement for the notion of quantum Markov states (QMS) on trees. A structure theorem for QMS on general trees is proved. We notice that any res…
Quantum Markov States on Cayley trees
Farrukh Mukhamedov, Abdessatar Souissi
It is known that any locally faithful quantum Markov state (QMS) on one dimensional setting can be considered as a Gibbs state associated with Hamiltonian with commuting nearest-ne…
Phase Transitions for quantum Ising model with competing XY -interactions on a Cayley tree
Farrukh Mukhamedov, Abdessatar Barhoumi, Abdessatar Souissi +1
The main aim of the present paper is to establish the existence of a phase transition for the quantum Ising model with competing XY interactions within the quantum Markov chain (QM…
Phase transitions for Quantum Markov Chains associated with Ising type models on a Cayley tree
Farrukh Mukhamedov, Abdessatar Barhoumi, Abdessatar Souissi
The main aim of the present paper is to prove the existence of a phase transition in quantum Markov chain (QMC) scheme for the Ising type models on a Cayley tree. Note that this ki…