Quantum Decoherence: A Logical Perspective

Fortín, Sebastián; Vanni, Leonardo

doi:10.1007/s10701-014-9805-1

Cited by 9 publications

(22 citation statements)

References 38 publications

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“…In other words, non-Boolean lattices can become Boolean under the action of special time evolutions. On the basis of this observation, in this work, we study the impact of a non unitary evolution on the logical structure of the system by continuing previous works [31]. That is, we study how the logical structure of quantum properties corresponding to relevant observables, becomes essentially Boolean by using an algebraic approach [17].…”

Section: Introductionmentioning

confidence: 92%

“…But the approach to quantum mechanics based on non-Hermitian operators offers a natural perspective in which these phenomena can be thought of as intrinsic. This alternative offers some computational advantages for certain examples, and at the same time, poses interesting philosophical discussions [31].…”

Section: Quantum Mechanics With Non-hermitian Hamiltonians In the Heimentioning

confidence: 99%

“…But it turns out that the quantumlogical approach has not addressed, up to now, the wholly important problem of characterizing the dynamical transformation in the logic of a system undergoing a decoherence process [29] and the reaching of the classical limit. As was shown in [31], the study of the classical limit offers the possibility of describing the transition from the quantum logic of a quantum system to the Boolean logic characteristic of a classical one. We will continue this line of research in this work by using nonHermitian time evolutions.…”

Section: Introductionmentioning

confidence: 99%

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Non-unitary Evolution of Quantum Logics

Fortín

Holik

Vanni

2016

Springer Proceedings in Physics

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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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Section: Introductionmentioning

confidence: 92%

Section: Quantum Mechanics With Non-hermitian Hamiltonians In the Heimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Non-unitary Evolution of Quantum Logics

Fortín

Holik

Vanni

2016

Springer Proceedings in Physics

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“…In a recent article it has been proved that SID can produce a process of this type in the case of systems with continuous energy spectrum (Fortin and Vanni 2014 …”

Section: Observables and Quantum Decoherencementioning

confidence: 99%

Classical Limit and Quantum Logic

2017

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The more common scheme to explain the classical limit of quantum mechanics includes decoherence, which removes from the state the interference terms classically inadmissible since embodying non-Booleanity. In this work we consider the classical limit from a logical viewpoint, as a quantum-to-Boolean transition. The aim is to open the door to a new study based on dynamical logics, that is, logics that change over time. In particular, we appeal to the notion of hybrid logics to describe semiclassical systems. Moreover, we consider systems with many characteristic decoherence times, whose sublattices of properties become distributive at different times.

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“…Among the several paths to understand the emergence of the classical world, Everett's relative-state interpretation [7,8,9,10,11,12] originated the decoherence theory [4,13,14,15,16,17,18,19,20,21,22,23] -the idea that it is the influence of the environment on the principal system and the measurement apparatus that causes the emergence of the classical world.…”

Section: Introductionmentioning

confidence: 99%

Understanding the pointer states

Brasil¹,

Castro²

2015

Eur. J. Phys.

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In quantum mechanics, pointer states are eigenstates of the observable of the measurement apparatus that represent the possible positions of the display pointer of the equipment. The origin of this concept lies in attempts to fill the blanks in the Everett's relative-state interpretation, and to make it a fully valid description of physical reality. To achieve this, it was necessary to consider not only the main system interacting with the measurement apparatus (like von Neumann and Everett did) but also the role of the environment in eliminating correlations between different possible measurements when interacting with the measurement apparatus. The interaction of the environment with the main system (and the measurement apparatus) is the core of the decoherence theory, which followed Everett's thesis. In this article, we review the measurement process according to von Neumann, Everett's relative state interpretation, the purpose of decoherence and some of its follow-up until Wojciech Zurek's primordial paper that consolidated the concept of pointer state, previously presented by Heinz Dieter Zeh. Employing a simple physical model consisting of a pair of two-level systems -one representing the main system, the other the measurement apparatus -and a thermal bath -representing the environment -we show how pointer states emerge, explaining its contributions to the question of measurement in quantum mechanics, as well as its limitations. Finally, we briefly show some of its consequences. This paper is accessible to readers with elementary knowledge about quantum mechanics, on the level of graduate courses.

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Quantum Decoherence: A Logical Perspective

Cited by 9 publications

References 38 publications

Non-unitary Evolution of Quantum Logics

Non-unitary Evolution of Quantum Logics

Classical Limit and Quantum Logic

Understanding the pointer states

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