title: Dynamical emergence of Markovianity in local time scheme.
abstract: Recently we pointed out the so-called local time scheme as a novel approach to quantum foundations that solves the preferred pointer-basis problem. In this paper, we introduce and analyse in depth a rather non-standard dynamical map that is imposed by the scheme. On the one hand, the map does not allow for introducing a properly defined generator of the evolution nor does it represent a quantum channel. On the other hand, the map is linear, positive, trace preserving and unital as well as completely positive, but is not divisible and therefore non-Markovian. Nevertheless, we provide quantitative criteria for dynamical emergence of time-coarse-grained Markovianity, for exact dynamics of an open system, as well as for operationally defined approximation of a closed or open many-particle system. A closed system never reaches a steady state, whereas an open system may reach a unique steady state given by the Lüders-von Neumann formula; where the smaller the open system, the faster a steady state is attained. These generic findings extend the standard open quantum systems theory and substantially tackle certain cosmological issues.
authors.affiliation: Department of Physics , Faculty of Sciences and Mathematics , 18000 Niš, Serbia.
authors.forename: J
authors.identifier: 0000-0002-4905-6457
authors.initials: J
authors.lastname: Jeknić-Dugić
authors.affiliation: Department of Physics , Faculty of Science , 34000 Kragujevac, Serbia.
authors.forename: M
authors.identifier: 0000-0003-4622-642X
authors.initials: M
authors.lastname: Arsenijević
authors.affiliation: Department of Physics , Faculty of Science , 34000 Kragujevac, Serbia.
authors.forename: M
authors.identifier: 0000-0002-4493-6009
authors.initials: M
authors.lastname: Dugić
keywords: Markovian processes; local time; quantum dynamical maps