In this work a quantum dynamical system is constituted by a von Neumann algebra , a unital Schwartz map and a -invariant normal faithful state on . We will prove that the ergodic properties of a quantum dynamical system are determined by its reversible part ; i.e. by a von Neumann sub-algebra of , with an automorphism and a normal state , as the restrictions on . Moreover, if 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.
@article{CML_2018__10_2_51_0, author = {Carlo Pandiscia}, title = {Reversible part of quantum dynamical systems: {A} review}, journal = {Confluentes Mathematici}, pages = {51--74}, publisher = {Institut Camille Jordan}, volume = {10}, number = {2}, year = {2018}, doi = {10.5802/cml.50}, mrnumber = {3928224}, language = {en}, url = {https://cml.centre-mersenne.org/articles/10.5802/cml.50/} }
TY - JOUR AU - Carlo Pandiscia TI - Reversible part of quantum dynamical systems: A review JO - Confluentes Mathematici PY - 2018 SP - 51 EP - 74 VL - 10 IS - 2 PB - Institut Camille Jordan UR - https://cml.centre-mersenne.org/articles/10.5802/cml.50/ DO - 10.5802/cml.50 LA - en ID - CML_2018__10_2_51_0 ER -
Carlo Pandiscia. Reversible part of quantum dynamical systems: A review. Confluentes Mathematici, Volume 10 (2018) no. 2, pp. 51-74. doi : 10.5802/cml.50. https://cml.centre-mersenne.org/articles/10.5802/cml.50/
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