Description of isolated macroscopic systems inside quantum mechanics

• Published in: Reports on mathematical physics Vol. 46; no. 1; pp. 191 - 202
• Main Authors: Lanz, L., Melsheimer, O., Vacchini, B.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-08-2000
• ISSN: 0034-4877; 1879-0674
• DOI: 10.1016/S0034-4877(01)80023-9

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,
t
0] a statistical operator is constructed as a solution of the Liouville—von Neumann equation, exhibiting at time
t the state parameters
ζ(
t′),
t
0 ≤
t′ ≤
t, and preparation parameters related to times
T ≤
t′ ≤
t
0. Relation with Zubarev's nonequilibrium 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.