Non-unitary Evolution of Quantum Logics

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Non-Hermitian Hamiltonians in Quantum Physics, ISSN: 0930-8989, Vol: 184, Page: 219-234

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Fortin, Sebastian; Holik, Federico; Vanni, Leonardo
Springer Nature
Physics and Astronomy
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book chapter description
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.