Description of isolated macroscopic systems inside quantum mechanics

Abstract

For an isolated macrosystem classical state parameters ζ(t) are introduced inside a quantum mechanical treatment. By a suitable mathematical representation of the actual preparation procedure in the time interval [T, t0] a statistical operator is constructed as a solution of the Liouville von Neumann equation, exhibiting at time t the state parameters ζ(t ′ ), t0 ≤ t ′ ≤ t, and preparation parameters related to times T ≤ t ′ ≤ t0. Relation with Zubarev's non-equilibrium statistical operator is discussed. A mechanism for memory loss is investigated and time evolution by a semigroup is obtained for a restricted set of relevant observables, slowly varying on a suitable time scale.

Master-Equations for the Study of Decoherence

“…In particular the description of macrosystems should rely on a suitable development of quantum statistical mechanics, which extended to non-equilibrium situations could allow for the appearance of a classical behavior for a subset of observables, possibly giving useful insights in the description of decoherence for a microsystem [3]. Since the connection between the phenomenon of decoherence and the measurement problem has been touched upon, it is important to stress that decoherence is not a solution to the aforementioned problem.…”

Quantum theory: the role of microsystems and macrosystems

“…Ludwig aims to a more comprehensive theory, which should provide in a natural way a state space for a macroscopic system. We shall now conclude this discussion indicating briefly a way we have taken to face this problem [30]. First of all let us stress a peculiar role that quantum field theory can have with respect to macrosystems.…”

Physics of a microsystem starting from nonequilibrium quantum statistical mechanics

“…We rely in the following on a general theory of an isolated macroscopic system inside quantum field theory that has been proposed in previous papers [6] and is very close to statistical mechanics formulated in terms of the non-equilibrium statistical operator by Zubarev and more recently by Morozov and Roepke [2], differing only in the introduction of a "preparation procedure" which extends over a finite time interval and refers to a confined isolated system, thus avoiding in principle the thermodynamic limit at the level of foundations of macroscopic physics. According to this theory a set of relevant variables is selected, slow enough on a suitable time scale, for which the very concept of isolation can make sense, built in terms of suitable field densities.…”

“…for t − t 0 > τ . Let us stress that for all observables  = Â(1) ⊗ Â( 2) such that [ Â( 1 ) , N1 ] = 0, [ Â( 2 ) , N2 ] = 0, (6) and these are the only meaningful observables for systems 1 and 2, ̺t is equivalent to the mixture ̺t = λ U (1) t−t0 ⊗ U (2) t−t0…”

“…In this connection the situation has improved relying on the concept of relevant variables and on the method of the non-equilibrium statistical operator [2]. In previous papers some improvement in the foundations of this concept was proposed insisting on the ideas of confinement, isolation and preparation of a macrosystem [6] during some initial time interval. A rather general and tractable situation, that we called "simple dynamics", arises if the evolution of the local relevant variables is driven by two-point Kubo correlation functions involving relevant variables and their currents at points separated by a short time interval: in other words memory contributions are assumed to be restricted to short time intervals.…”