Jeknić-Dugić J, Arsenijević M, Dugić M
Department of Physics , Faculty of Sciences and Mathematics , 18000 Niš, Serbia.
Department of Physics , Faculty of Science , 34000 Kragujevac, Serbia.
Proc Math Phys Eng Sci. 2016 Jun;472(2190):20160041. doi: 10.1098/rspa.2016.0041.
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.
最近，我们指出了所谓的局部时间方案，它是一种解决优选指针基问题的量子基础新方法。在本文中，我们深入介绍并分析了该方案所施加的一种相当非标准的动力学映射。一方面，该映射不允许引入恰当定义的演化生成元，也不代表量子信道。另一方面，该映射是线性的、正定的、保迹且幺正的，同时也是完全正定的，但不可分解，因此是非马尔可夫的。尽管如此，我们为时间粗粒化马尔可夫性的动力学出现、开放系统的精确动力学以及封闭或开放多粒子系统的操作定义近似提供了定量标准。封闭系统永远不会达到稳态，而开放系统在吕德斯 - 冯·诺伊曼公式给出的情况下可能达到唯一的稳态；开放系统越小，达到稳态的速度就越快。这些一般性发现扩展了标准的开放量子系统理论，并在很大程度上解决了某些宇宙学问题。
