Nonlinear map**s appear throughout mathematics, and their range of applications is
immense, including the theory of differential equations, the theory of probability, the theory of …

The problem of recurrence for quantum Markov chains on trees (QMCT), is more subtle than
for 1D quantum Markov chains (QMC); it involves infinitely many rays due to the exponential …

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 …

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 …

We study a mixing condition for entangled Markov chains, so-called ψ-mixing property. We
prove that every entangled Markov chain, whose Markov operators satisfy the Markov …

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 kind …

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 …

In this paper, we continue the investigation of quantum Markov states (QMS) and define their
mean entropies. Such entropies are explicitly computed under certain conditions. The …

It is known that the disordered phase of the classical Ising model on the Caley tree is
extreme in some region of the temperature. If one considers the Ising model with competing …

In this paper we construct (nonhomogeneous) quantum Markov chains associated with open
quantum random walks. The quantum Markov chain, like the classical Markov chain, is a …