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Non-Hermitian Hamiltonians in Quantum Physics pp 219–234Cite as

Non-unitary Evolution of Quantum Logics

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Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 184))

Abstract

In this work we present a dynamical approach to quantum logics. By changing the standard formalism of quantum mechanics to allow non-Hermitian operators as generators of time evolution, we address the question of how can logics evolve in time. In this way, we describe formally how a non-Boolean algebra may become a Boolean one under certain conditions. We present some simple models which illustrate this transition and develop a new quantum logical formalism based in complex spectral resolutions, a notion that we introduce in order to cope with the temporal aspect of the logical structure of quantum theory.

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Notes

  1. 1.

    We do not consider the Khalfin mode since it has an extremely long decaying time [47, 48].

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Author information

Authors and Affiliations

  1. CONICET - Department of Physics, Universidad de Buenos Aires, Buenos Aires, Argentina

    Sebastian Fortin & Leonardo Vanni

  2. Instituto de Física La Plata, CONICET & Departamento de Física, UNLP, La Plata, Argentina

    Federico Holik

Authors
  1. Sebastian Fortin
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  2. Federico Holik
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  3. Leonardo Vanni
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Corresponding author

Correspondence to Sebastian Fortin .

Editor information

Editors and Affiliations

  1. Dipartimento di Energia, Università degli Studi di Palermo, Palermo, Italy

    Fabio Bagarello

  2. Dipartimento di Fisica e Chimica, Università degli Studi di Palermo, Palermo, Palermo, Italy

    Roberto Passante

  3. Matematica e Informatica, Università degli Studi di Palermo, Palermo, Italy

    Camillo Trapani

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Fortin, S., Holik, F., Vanni, L. (2016). Non-unitary Evolution of Quantum Logics. In: Bagarello, F., Passante, R., Trapani, C. (eds) Non-Hermitian Hamiltonians in Quantum Physics. Springer Proceedings in Physics, vol 184. Springer, Cham. https://doi.org/10.1007/978-3-319-31356-6_14

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