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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 restriction of QMS in the sense of Ref. cite{AccFid03} is not necessarily to be a QMS. It turns out that localized QMS has the mentioned property which is called textit{sub-Markov states}, this allows us to characterize translation invariant QMS on regular trees.
We introduce quantum Markov states (QMS) in a general tree graph $G= (V, E)$, extending the Cayley trees case. We investigate the Markov property w.r.t. the finer structure of the considered tree. The main result of this paper concerns the diagonaliz
Using the Trotter-Kato theorem we prove the convergence of the unitary dynamics generated by an increasingly singular Hamiltonian in the case of a single field coupling. The limit dynamics is a quantum stochastic evolution of Hudson-Parthasarathy typ
We give a mathematically rigorous derivation of Ehrenfests equations for the evolution of position and momentum expectation values, under general and natural assumptions which include atomic and molecular Hamiltonians with Coulomb interactions.
In this paper, we consider the classical Ising model on the Cayley tree of order k and show the existence of the phase transition in the following sense: there exists two quantum Markov states which are not quasi-equivalent. It turns out that the fou
A version of Connes trace formula allows to associate a measure on the essential spectrum of a Schrodinger operator with bounded potential. In solid state physics there is another celebrated measure associated with such operators --- the density of s