Spectral and ergodic properties of completely positive maps and decoherence



Fidaleo, Francesco, Ottomano, Federico and Rossi, Stefano
(2022) Spectral and ergodic properties of completely positive maps and decoherence. Linear Algebra and its Applications, 633. pp. 104-126.

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Abstract

In an attempt to propose more general conditions for decoherence to occur, we study spectral and ergodic properties of unital, completely positive maps on not necessarily unital C⁎-algebras, with a particular focus on gapped maps for which the transient portion of the arising dynamical system can be separated from the persistent one. After some general results, we first devote our attention to the abelian case by investigating the unital ⁎-endomorphisms of, in general non-unital, C⁎-algebras, and their spectral structure. The finite-dimensional case is also investigated in detail, and examples are provided of unital completely positive maps for which the persistent part of the associated dynamical system is equipped with the new product making it into a C⁎-algebra, and the map under consideration restricts to a unital ⁎-automorphism for this new C⁎-structure, thus generating a conservative dynamics on that persistent part.

Item Type: Article
Uncontrolled Keywords: Operator algebras, Completely positive maps, Spectrum, Decoherence
Divisions: Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User: Symplectic Admin
Date Deposited: 05 Nov 2021 11:51
Last Modified: 18 Jan 2023 21:25
DOI: 10.1016/j.laa.2021.10.007
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3142857