2016/06/15 by Carlo Pandiscia, Pandiscia, Carlo
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.1606.04910
openalex publication_date 2016/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work a quantum dynamical system (\mathfrak M,Φ, φ) is constituted by a von Neumann algebra \mathfrak M, by a unital Schwartz map Φ:\mathfrakM→ M and by a Φ-invariant normal faithful state φ on \mathfrak M. The ergodic properties of a quantum dynamical system, depends on its reversible part (\mathfrakD_∞,Φ_∞, φ_∞). It is constituted by a von Neumann sub-algebra \mathfrakD_∞ of \mathfrak M by an automorphism Φ_∞ and a normal state φ_∞, the restrictions of Φ and φ on \mathfrakD_∞ respectively. Moreover, if \mathfrakD_∞ is a trivial algebra the quantum dynamical system is ergodic. Furthermore we will give some properties of the reversible part of quantum dynamical system, in particular, we will study its relationships with the canonical decomposition of Nagy-Fojas of linear contraction related to the quantum dynamical system.