Reversible part of quantum dynamical systems: A review
Confluentes Mathematici, Volume 10 (2018) no. 2, pp. 51-74.

In this work a quantum dynamical system (ūĚĒź,ő¶,Ōē) is constituted by a von Neumann algebra ūĚĒź, a unital Schwartz map ő¶:ūĚĒź‚ÜíūĚĒź and a ő¶-invariant normal faithful state Ōē on ūĚĒź. We will prove that the ergodic properties of a quantum dynamical system are determined by its reversible part (ūĚĒá ‚ąě ,ő¶ ‚ąě ,Ōē ‚ąě ); i.e. by a von Neumann sub-algebra ūĚĒá ‚ąě of ūĚĒź, with an automorphism ő¶ ‚ąě and a normal state Ōē ‚ąě , as the restrictions on ūĚĒá ‚ąě . Moreover, if ūĚĒá ‚ąě is a trivial algebra, then the quantum dynamical system is ergodic. Furthermore, we will show some properties of reversible part of the quantum dynamical system, finally we will study its relations with the canonical decomposition of Nagy-Fojas of linear contraction related to a quantum dynamical system.

Received:
Accepted:
Published online:
DOI: 10.5802/cml.50
Classification: 46L07,  46L55,  81S22
Keywords: Quantum dynamical system, Multiplicative core, Algebra of effective observables.
Pandiscia, Carlo 1

1 Centro Vito Volterra, Università di Roma Tor Vergata, Via Columbia 2, Roma 00133, Italy
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Pandiscia, Carlo. Reversible part of quantum dynamical systems: A review. Confluentes Mathematici, Volume 10 (2018) no. 2, pp. 51-74. doi : 10.5802/cml.50. http://www.numdam.org/articles/10.5802/cml.50/

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