Decoherence in infinite quantum systems

Blanchard, Philippe; Hellmich, Mario

doi:10.1063/1.4746056

Cited by 2 publications

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References 108 publications

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“…We have a (maximal) reversible quantum dynamical systems It is clear that D ∞ is Φ k -invariant for all integers k and is invariant under automorphism group σ ϕ t and by previous decomposition theorem we can say that (see [4] theorem 6):…”

Section: Decomposition Theoremmentioning

confidence: 99%

Reversible part of quantum dynamical systems: A review

Pandiscia¹

2019

Confluentes Mathematici

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In this work a quantum dynamical system (M, Φ, ϕ) is constituted by a von Neumann algebra M, by a unital Schwartz map Φ : M → M and by a Φ-invariant normal faithful state ϕ on M. We prove that the ergodic properties of a quantum dynamical system, are determined by its reversible part (D ∞ , Φ ∞ , ϕ ∞ ). It is constituted by a von Neumann sub-algebra D ∞ of M by an automorphism Φ ∞ and a normal state ϕ ∞ , the restrictions of Φ and ϕ on D ∞ respectively. Moreover, if D ∞ is a trivial algebra then 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 relations with the canonical decomposition of Nagy-Fojas of linear contraction related to the quantum dynamical system.

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Section: Decomposition Theoremmentioning

confidence: 99%

Reversible part of quantum dynamical systems: A review

Pandiscia¹

2019

Confluentes Mathematici

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Classical and Quantum Probability: The Two Logics of Science

Blanchard

2015

On Thinking

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We review and discuss first briefly the algebraic framework of classical and quantum physics and commutative and noncommutative probability theory. After that we propose a mathematical definition of decoherence sufficiently general to accommodate quantum systems with infinitely many degrees of freedom and give an exhaustive list of possible scenarios that can emerge due to decoherence. We conclude with some messages of quantum science.

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Decoherence in infinite quantum systems

Cited by 2 publications

References 108 publications

Reversible part of quantum dynamical systems: A review

Reversible part of quantum dynamical systems: A review

Classical and Quantum Probability: The Two Logics of Science

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