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  • 1.
    Asano, Masanari
    et al.
    Tokuyama College of Technology, Japan.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ohya, Masanori
    Tokyo University of Science, Japan.
    Tanaka, Yoshiharu
    Tokyo University of Science, Japan.
    Yamato, Ichiro
    Tokyo University of Science, Japan.
    Three-body system metaphor for the two-slit experiment and Escherichia coli lactose-glucose metabolism2016In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 374, no 2068, article id 20150243Article in journal (Refereed)
    Abstract [en]

    We compare the contextual probabilistic structures of the seminal two-slit experiment (quantum interference experiment), the system of three interacting bodies and Escherichia coli lactose-glucose metabolism. We show that they have the same non-Kolmogorov probabilistic structure resulting from multi-contextuality. There are plenty of statistical data with non-Kolmogorov features; in particular, the probabilistic behaviour of neither quantum nor biological systems can be described classically. Biological systems (even cells and proteins) are macroscopic systems and one may try to present a more detailed model of interactions in such systems that lead to quantum-like probabilistic behaviour. The system of interactions between three bodies is one of the simplest metaphoric examples for such interactions. By proceeding further in this way (by playing with n-body systems) we shall be able to find metaphoric mechanical models for complex bio-interactions, e.g. signalling between cells, leading to non-Kolmogorov probabilistic data.

  • 2.
    Bagarello, F.
    et al.
    Univ Palermo, Italy ; INFN, Italy.
    Haven, E.
    Univ Leicester, UK.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics. Natl Res Univ Informat Technol Mech & Opt ITMO, Russia.
    A model of adaptive decision-making from representation of information environment by quantum fields2017In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 375, no 2106, article id 20170162Article in journal (Refereed)
    Abstract [en]

    We present the mathematical model of decisionmaking (DM) of agents acting in a complex and uncertain environment (combining huge variety of economical, financial, behavioural and geopolitical factors). To describe interaction of agents with it, we apply the formalism of quantum field theory (QTF). Quantum fields are a purely informational nature. The QFT model can be treated as a far relative of the expected utility theory, where the role of utility is played by adaptivity to an environment (bath). However, this sort of utility- adaptivity cannot be represented simply as a numerical function. The operator representation in Hilbert space is used and adaptivity is described as in quantum dynamics. We are especially interested in stabilization of solutions for sufficiently large time. The outputs of this stabilization process, probabilities for possible choices, are treated in the framework of classical DM. To connect classical and quantum DM, we appeal to Quantum Bayesianism. We demonstrate the quantumlike interference effect in DM, which is exhibited as a violation of the formula of total probability, and hence the classical Bayesian inference scheme. This article is part of the themed issue 'Second quantum revolution: foundational questions'.

  • 3.
    D'Ariano, Giacomo Mauro
    et al.
    Univ Pavia, Italy.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Preface of the special issue quantum foundations: information approach2016In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 374, no 2068, article id 20150244Article in journal (Other academic)
    Abstract [en]

    This special issue is based on the contributions of a group of top experts in quantum foundations and quantum information and probability. It enlightens a number of interpretational, mathematical and experimental problems of quantum theory.

  • 4.
    Haven, Emmanuel
    et al.
    Univ Leicester, UK.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Quantum probability and the mathematical modelling of decision-making2016In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 374, no 2058, article id 20150105Article in journal (Other academic)
  • 5.
    Holmqvist, Cecilia
    et al.
    Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering.
    Belzig, Wolfgang
    Fogelström, Mikael
    Non-equilibrium charge and spin transport in superconducting–ferromagnetic–superconducting point contacts2018In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 376, no 2125, article id 20150229Article in journal (Refereed)
    Abstract [en]

    The conventional Josephson effect may be modified by introducing spin-active scattering in the interface layer of the junction. Here, we discuss a Josephson junction consisting of two s-wave superconducting leads coupled over a classical spin that precesses with the Larmor frequency due to an external magnetic field. This magnetically active interface results in a time-dependent boundary condition with different tunnelling amplitudes for spin-up and -down quasi- particles and where the precession produces spin-flip scattering processes. As a result, the Andreev states develop sidebands and a non-equilibrium population that depend on the details of the spin precession. The Andreev states carry a steady-state Josephson charge current and a time-dependent spin current, whose current–phase relations could be used to characterize the precessing spin. The spin current is supported by spin-triplet correlations induced by the spin precession and creates a feedback effect on the classical spin in the form of a torque that shifts the precession frequency. By applying a bias voltage, the Josephson frequency adds another complexity to the situation and may create resonances together with the Larmor frequency. These Shapiro resonances manifest as torques and, under suitable 2conditions, are able to reverse the direction of the classical spin in sub-nanosecond time. Another characteristic feature is the subharmonic gap structure in the DC charge current displaying an even–odd effect attributable to precession-assisted multiple Andreev reflections. This article is part of the theme issue ‘Andreev bound states’.

  • 6.
    Jaeger, Gregg
    et al.
    Boston Univ, USA.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Perinotti, Paolo
    Univ Pavia, Italy.
    Preface for the special issue, 'Second quantum revolution: foundational questions'2017In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 375, no 2106, article id 20160397Article in journal (Other academic)
  • 7.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Quantum Bayesianism as the basis of general theory of decision-making2016In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 374, no 2068, article id 20150245Article in journal (Refereed)
    Abstract [en]

    We discuss the subjective probability interpretation of the quantum-like approach to decision making and more generally to cognition. Our aim is to adopt the subjective probability interpretation of quantum mechanics, quantum Bayesianism (QBism), to serve quantum-like modelling and applications of quantum probability outside of physics. We analyse the classical and quantum probabilistic schemes of probability update, learning and decision-making and emphasize the role of Jeffrey conditioning and its quantum generalizations. Classically, this type of conditioning and corresponding probability update is based on the formula of total probability-one the basic laws of classical probability theory.

  • 8.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    'Social Laser': action amplification by stimulated emission of social energy2016In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 374, no 2058, article id 20150094Article in journal (Refereed)
    Abstract [en]

    The problem of the 'explanation' of recent social explosions, especially in the Middle East, but also in Southern Europe and the USA, has been debated actively in the social and political literature. We can mention the contributions of P. Mason, F. Fukuyama, E. Schmidt, J. Cohen and I. Krastev to this debate. We point out that the diversity of opinions and conclusions is really amazing. At the moment, there is no consistent and commonly acceptable theory of these phenomena. We present a model of social explosions based on a novel approach for the description of social processes, namely the quantum-like approach. Here quantum theory is treated simply as an operational formalism-without any direct relation to physics. We explore the quantum-like laser model to describe the possibility of action amplification by stimulated emission of social energy.

  • 9.
    Lozada Aguilar, Miguel Angel
    et al.
    Aseguramiento Tecnol Pemex Explorac & Prod, Mexico.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Oleschko, Klaudia
    Univ Nacl Autonoma Mexico, Mexico.
    From axiomatics of quantum probability to modelling geological uncertainty and management of intelligent hydrocarbon reservoirs with the theory of open quantum systems2018In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 376, no 2118, article id 20170225Article in journal (Refereed)
    Abstract [en]

    As was recently shown by the authors, quantum probability theory can be used for the modelling of the process of decision-making (e.g. probabilistic risk analysis) for macroscopic geophysical structures such as hydrocarbon reservoirs. This approach can be considered as a geophysical realization of Hilbert's programme on axiomatization of statistical models in physics (the famous sixth Hilbert problem). In this conceptual paper, we continue development of this approach to decision-making under uncertainty which is generated by complexity, variability, heterogeneity, anisotropy, as well as the restrictions to accessibility of subsurface structures. The belief state of a geological expert about the potential of exploring a hydrocarbon reservoir is continuously updated by outputs of measurements, and selection of mathematical models and scales of numerical simulation. These outputs can be treated as signals Dfrom the information environment E. The dynamics of the belief state can be modelled with the aid of the theory of open quantum systems: a quantum state (representing uncertainty in beliefs) is dynamically modified through coupling with E; stabilization to a steady state determines a decision strategy. In this paper, the process of decision-making about hydrocarbon reservoirs (e.g. 'explore or not?'; 'open new well or not?'; 'contaminated by water or not?'; 'double or triple porosity medium?') is modelled by using the Gorini-Kossakowski- Sudarshan-Lindblad equation. In our model, this equation describes the evolution of experts' predictions about a geophysical structure. We proceed with the information approach to quantum theory and the subjective interpretation of quantum probabilities (due to quantum Bayesianism).

  • 10.
    Lozada Aguilar, Miguel Angel
    et al.
    Aseguramiento Tecnol Pemex Explorac & Prod, Mexico.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Oleschko, Klaudia
    UNAM, Mexico.
    de Jesus Correa, Maria
    Suptcia Caracterizac Yacimientos, Mexico.
    Quantum Bayesian perspective for intelligence reservoir characterization, monitoring and management2017In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 375, no 2106, article id 20160398Article in journal (Refereed)
    Abstract [en]

    The paper starts with a brief review of the literature about uncertainty in geological, geophysical and petrophysical data. In particular, we present the viewpoints of experts in geophysics on the application of Bayesian inference and subjective probability. Then we present arguments that the use of classical probability theory (CP) does not match completely the structure of geophysical data. We emphasize that such data are characterized by contextuality and non-Kolmogorovness (the impossibility to use the CP model), incompleteness as well as incompatibility of some geophysical measurements. These characteristics of geophysical data are similar to the characteristics of quantum physical data. Notwithstanding all this, contextuality can be seen as a major deviation of quantum theory from classical physics. In particular, the contextual probability viewpoint is the essence of the Vaxjo interpretation of quantum mechanics. We propose to use quantum probability (QP) for decision-making during the characterization, modelling, exploring and management of the intelligent hydrocarbon reservoir. Quantum Bayesianism (QBism), one of the recently developed information interpretations of quantum theory, can be used as the interpretational basis for such QP decision-making in geology, geophysics and petroleum projects design and management. This article is part of the themed issue ` Second quantum revolution: foundational questions'.

  • 11.
    Rashkovskiy, Sergey
    et al.
    RAS Ishlinsky Inst Problems Mech, Russia;Tomsk State Univ, Russia.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics. Natl Res Univ Informat Technol Mech & Opt ITMO, Russia.
    Generalized Fock space and contextuality2019In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 377, no 2157, article id 20190096Article in journal (Refereed)
    Abstract [en]

    This paper is devoted to linear space representations of contextual probabilities-in generalized Fock space. This gives the possibility to use the calculus of creation and annihilation operators to express probabilistic dynamics in the Fock space (in particular, the wide class of classical kinetic equations). In this way, we reproduce the Doi-Peliti formalism. The context-dependence of probabilities can be quantified with the aid of the generalized formula of total probability-by the magnitude of the interference term. This article is part of the theme issue 'Contextuality and probability in quantum mechanics and beyond'.

1 - 11 of 11
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