Description of isolated macroscopic systems inside quantum mechanics

Abstract

For an isolated macrosystem classical state parameters $\zeta (t)$ are introduced inside a quantum mechanical treatment. By a suitable mathematical representation of the actual preparation procedure in the time interval $[T,t_0]$ a statistical operator is constructed as a solution of the Liouville von Neumann equation, exhibiting at time $t$ the state parameters $\zeta (t^{\prime })$, $t_0\le t^{\prime }\le t$, and {\it preparation parameters} related to times $T\le t^{\prime }\le t_0$. 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.

13 pages, latex, romp31 style, no figures, to appear in the Proceedings of the XXXI Symposium on Mathematical Physics (Torun, Poland), to be published in Rep. Math. Phys

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