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...

Following on from the notion of (first-order) causality, which generalises the notion of being tracepreserving from CP-maps to abstract processes, we give a characterization for the most general kind of map which sends causal processes to causal processes. These new, second-order causal processes enable us to treat the input processes as ‘local laboratories’ whose causal ordering needs not be f...

Classical results in the theory of monotone semiflows give sufficient conditions for the generic solution to converge toward an equilibrium or towards the set of equilibria (quasiconvergence). In this paper, we provide new formulations of these results in terms of the measure-theoretic notion of prevalence, developed in [1, 8]. For monotone reaction-diffusion systems with Neumann boundary condi...

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 ...

Let A' be a compact C -manifold. Let || ||, || || denote the supremum norm and the C -norm, respectively, and let \P \ be a Markovian semigroup on C(X). The semigroup's infinitesimal generator A, with domain 3), is defined by Af= lim Q t~ (P'f f), whenever the limit exists in || ||. Theorem. Assume that \P s preserves C -junctions and that the restriction of {PA to C2(X), I I' is strongly conti...

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...