The concept of time-coarsened density matrix for open systems has frequently featured in equilibrium and non-equilibrium statistical mechanics, without being probed as to the detailed consequences of the time averaging procedure. In this work we introduce and prove the need for a selective and non-uniform time-sampling, whose form depends on the properties of the bath. It is also applicable when an open microscopic sub-system is coupled to another finite system. By use of a time-periodic minimal coupling model between these two (...) systems, we present detailed quantitative consequences of time coarsening, which include initial state independence of equilibration, deviations from long term averages, their environment size dependence and the approach to classicality, as measured by a Leggett–Garg type inequality. An interacting multiple qubit model affords comparison between the time integrating procedure and the more conventional environment tracing method. (shrink)

An expression of the Lindbladian form is proposed that ensures an unambiguous time-continuous reduction of the initial system-pointer wave-packet to one in which the readings and the observable’s values are aligned, formalized as the transition from an outer product to an inner product of the system’s and apparatus’ density matrices. The jump operators are in the basis of the observables, with uniquely determined parameters derived from the measurement set-up (thereby differing from S. Weinberg’s Lindbladian resolution of wave-packet formalism) and conforming (...) to Born’s probability rules. The novelty lies in formalising the adaptability of the surroundings (including the measuring device) to the mode of observation. Accordingly, the transition is of finite duration (in contrast to its instantaneousness in the von Neumann’s formulation). This duration is estimated for a simple half-spin-like model. (shrink)