In this paper, entangled K-meson model and decoherence phenomenon in thesystem is studied. Using Lindblad equation, dynamical equation of systemthat interacts with the environment obtained. We find that non-Hermitian Hamiltonian ofthe system makes completely positive trace-preserving map (CPT-map) on space ofdensity matrix does not satisfy trace preserving properties. also purity densitymatrix ...

Let pX,μq be a standard probability space. An automorphism T of this space has the weak Pinsker property if for every ε ą 0 it is isomorphic to a direct product of a Bernoulli shift and an automorphism of entropy less than ε. This property was introduced by Thouvenot, who conjectured that it holds for all measure-preserving systems. This paper proves Thouvenot’s conjecture. The proof applies wi...

For M and N closed oriented connected smooth manifolds of the same dimension, we consider the mapping space Map(M, N ; f) of continuous maps homotopic to f : M → N . We will show that the evaluation map from the space of maps to the manifold N induces a nontrivial homomorphism on the fundamental group only if the self coincidence number of f , denoted Λf,f , equals zero. Since Λf,f is equal to ...

The relation between the two notions quasifactors and joinings is investigated and the notion of a joining quasifactor is introduced. We clarify the close connection between quasifactors and symmetric infinite selfjoinings which arises from de Finetti-Hewitt-Savage theorem. Unlike the zero entropy case where quasifactors seems to preserve some properties of their parent system, it is shown that...

For a measure-preserving transformation T which is a skew-product of a measure-preserving transformation S and a topological group endomorphism a, it is shown that the entropy h satisfies the following "addition theorem": h(T) = h(S) + h(o). Introduction. In a previous paper [4], conditions were given for a certain type of transformation of a G-space (G being a compact separable group) to have ...

Let B(X ) be the algebra of all bounded linear operators on a complex Banach space X and let I(X ) be the set of non-zero idempotent operators in B(X ). A surjective map φ : B(X ) → B(X ) preserves nonzero idempotency of the Jordan products of two operators if for every pair A, B ∈ B(X ), the relation AB +BA ∈ I(X ) implies φ(A)φ(B)+φ(B)φ(A) ∈ I(X ). In this paper, the structures of linear surj...