lnu.sePublications
Change search
Link to record
Permanent link

Direct link
BETA
Publications (10 of 435) Show all publications
Antoniouk, A. V., Oleschko, K., Kochubei, A. N. & Khrennikov, A. (2018). A stochastic p-adic model of the capillary flow in porous random medium. Physica A: Statistical Mechanics and its Applications, 505, 763-777
Open this publication in new window or tab >>A stochastic p-adic model of the capillary flow in porous random medium
2018 (English)In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 505, p. 763-777Article in journal (Refereed) Published
Abstract [en]

We develop the p-adic model of propagation of fluids (e.g., oil or water) in capillary networks in a porous random medium. The hierarchic structure of a system of capillaries is mathematically modeled by endowing trees of capillaries with the structure of an ultra metric space. Considerations are restricted to the case of idealized networks represented by homogeneous p-trees with p branches leaving each vertex, where p > 1 is a prime number. Such trees are realized as the fields of p-adic numbers. We introduce and study an inhomogeneous Markov process describing the penetration of fluid into a porous random medium. (C) 2018 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
Elsevier, 2018
Keywords
P-adic numbers, P-adic theoretical physics, Porous random medium, Capillary network, Penetration of fluid, Inhomogeneous Markov process
National Category
Physical Sciences Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-76948 (URN)10.1016/j.physa.2018.03.049 (DOI)000437061000067 ()
Available from: 2018-07-19 Created: 2018-07-19 Last updated: 2018-07-19Bibliographically approved
Baladron, C. & Khrennikov, A. (2018). At the Crossroads of Three Seemingly Divergent Approaches to Quantum Mechanics. In: A. Khrennikov, B. Toni (Ed.), Quantum Foundations, Probability and Information: (pp. 13-21). Springer
Open this publication in new window or tab >>At the Crossroads of Three Seemingly Divergent Approaches to Quantum Mechanics
2018 (English)In: Quantum Foundations, Probability and Information / [ed] A. Khrennikov, B. Toni, Springer, 2018, p. 13-21Chapter in book (Refereed)
Abstract [en]

Several concepts stemming from three apparently divergent approaches to quantum mechanics—Bohmian Mechanics, QBism, and Time-Symmetric Quantum Mechanics—are interwoven in an information-theoretic Darwinian scheme applied to fundamental physical systems that might contribute to shed light on some long-standing quantum mechanical conundrums.

Place, publisher, year, edition, pages
Springer, 2018
Series
STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health, ISSN 2520-193X
Keywords
Quantum mechanical foundations; Darwinian evolution; Adaptive dynamics; Quantum information; Information theory
National Category
Computational Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-79083 (URN)10.1007/978-3-319-74971-6_2 (DOI)978-3-319-74970-9 (ISBN)978-3-319-74971-6 (ISBN)
Available from: 2018-12-05 Created: 2018-12-05 Last updated: 2018-12-11Bibliographically approved
Khrennikov, A. & Loubenets, E. R. (2018). Evaluating the Maximal Violation of the Original Bell Inequality by Two-Qudit States Exhibiting Perfect Correlations/Anticorrelations. Entropy, 20(11), Article ID 829.
Open this publication in new window or tab >>Evaluating the Maximal Violation of the Original Bell Inequality by Two-Qudit States Exhibiting Perfect Correlations/Anticorrelations
2018 (English)In: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 20, no 11, article id 829Article in journal (Refereed) Published
Abstract [en]

We introduce the general class of symmetric two-qubit states guaranteeing the perfect correlation or anticorrelation of Alice and Bob outcomes whenever some spin observable is measured at both sites. We prove that, for all states from this class, the maximal violation of the original Bell inequality is upper bounded by 32" role="presentation">32 and specify the two-qubit states where this quantum upper bound is attained. The case of two-qutrit states is more complicated. Here, for all two-qutrit states, we obtain the same upper bound 32" role="presentation">32 for violation of the original Bell inequality under Alice and Bob spin measurements, but we have not yet been able to show that this quantum upper bound is the least one. We discuss experimental consequences of our mathematical study.

Place, publisher, year, edition, pages
MDPI, 2018
Keywords
original Bell inequality; perfect correlation/anticorrelation; qudit states; quantum bound; measure of classicality
National Category
Computational Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-79077 (URN)10.3390/e20110829 (DOI)
Available from: 2018-12-05 Created: 2018-12-05 Last updated: 2018-12-10Bibliographically approved
Khrennikov, A. (2018). External Observer Reflections on QBism, Its Possible Modifications, and Novel Applications. In: A. Khrennikov, B. Toni (Ed.), Quantum Foundations, Probability and Information: (pp. 93-118). Springer
Open this publication in new window or tab >>External Observer Reflections on QBism, Its Possible Modifications, and Novel Applications
2018 (English)In: Quantum Foundations, Probability and Information / [ed] A. Khrennikov, B. Toni, Springer, 2018, p. 93-118Chapter in book (Refereed)
Abstract [en]

In this critical essay, I present my personal reflections on QBism. I have no intrinsic sympathy neither to QBism nor to subjective interpretation of probability in general. However, I have been following the development of QBism from its very beginning, observing its evolution and success, sometimes with big surprise. Therefore my reflections on QBism can be treated as “external observer” reflections. I hope that my view on this interpretation of quantum mechanics (QM) has some degree of objectivity. It may be useful for researchers who are interested in quantum foundations, but do not belong to the QBism community, because I tried to analyze essentials of QBism critically (i.e., not just emphasizing its advantages, as in a typical QBist publication). QBists, too, may be interested in comments of an external observer who monitored development of this approach to QM during the last 16 years. (However, this paper cannot serve as an introduction to QBism. It neither concerns the philosophic issues around QBism.) Two sections are devoted to comparison of QBism with two interpretations of QM, the Växjö and information interpretations, which are close to QBism in two very different aspects, probabilistic and informational. The second part of the paper is devoted to interpretations of probability, objective versus subjective, and views of Kolmogorov, von Mises, and de Finetti. De Finetti’s approach to methodology of science is presented and compared with QBism. One of the outputs of this comparison is understanding of restrictiveness of QBism, where the subjective probability viewpoint is applied only to QM. One of the main messages of this paper is that QBism has to be completed by CBism (classical physics Bayesianism). Finally, the possibility to use QBism as the general interpretational basis for applications of the quantum probabilistic formalism for decision-making outside of physics (in cognitive, social, and political sciences, psychology, economics, finances) is considered.

Place, publisher, year, edition, pages
Springer, 2018
Series
STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health, ISSN 2520-193X, E-ISSN 2520-1948
National Category
Other Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-79082 (URN)10.1007/978-3-319-74971-6_9 (DOI)978-3-319-74970-9 (ISBN)978-3-319-74971-6 (ISBN)
Available from: 2018-12-05 Created: 2018-12-05 Last updated: 2018-12-10Bibliographically approved
Lozada Aguilar, M. A., Khrennikov, A. & Oleschko, K. (2018). From axiomatics of quantum probability to modelling geological uncertainty and management of intelligent hydrocarbon reservoirs with the theory of open quantum systems. Philosophical Transactions. Series A: Mathematical, physical, and engineering science, 376(2118), Article ID 20170225.
Open this publication in new window or tab >>From axiomatics of quantum probability to modelling geological uncertainty and management of intelligent hydrocarbon reservoirs with the theory of open quantum systems
2018 (English)In: 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) Published
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).

Keywords
decision-making and risk analysis, geology, Hilbert's sixth problem, quantum versus classical Bayesian inference, heterogeneity, open quantum systems
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-76464 (URN)10.1098/rsta.2017.0225 (DOI)000427878700004 ()29555799 (PubMedID)
Available from: 2018-07-10 Created: 2018-07-10 Last updated: 2018-07-10Bibliographically approved
Haven, E., Khrennikov, A., Ma, C. & Sozzo, S. (2018). Introduction to quantum probability theory and its economic applications. Journal of Mathematical Economics, 78, 127-130
Open this publication in new window or tab >>Introduction to quantum probability theory and its economic applications
2018 (English)In: Journal of Mathematical Economics, ISSN 0304-4068, E-ISSN 1873-1538, Vol. 78, p. 127-130Article in journal, Editorial material (Other academic) Published
Place, publisher, year, edition, pages
Elsevier, 2018
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-78740 (URN)10.1016/j.jmateco.2018.08.004 (DOI)000448495000015 ()
Available from: 2018-11-08 Created: 2018-11-08 Last updated: 2018-11-08Bibliographically approved
Melkikh, A. V. & Khrennikov, A. (2018). Mechanisms of directed evolution of morphological structures and the problems of morphogenesis. Biosystems (Amsterdam. Print), 168, 26-44
Open this publication in new window or tab >>Mechanisms of directed evolution of morphological structures and the problems of morphogenesis
2018 (English)In: Biosystems (Amsterdam. Print), ISSN 0303-2647, E-ISSN 1872-8324, Vol. 168, p. 26-44Article, review/survey (Refereed) Published
Abstract [en]

Morphogenesis mechanisms are considered from the point of view of complexity. It has been shown that the presence of long-range interactions between biologically important molecules is a necessary condition for the formation and stable operation of morphological structures. A quantum model of morphogenesis based on non-Archimedean analysis and the presence of long-range interactions between biologically important molecules has been constructed. This model shows that the evolution of morphological structures essentially depends on the availability of a priori information on these structures. Critical steps in evolution related to the most important morphological and behavioral findings have been analyzed; the results have shown that the implementation of such steps can only be explained within the framework of a partially directed evolution. Thus, the previously proposed model for a partially directed evolution is established for modeling the evolution of morphological structures.

Place, publisher, year, edition, pages
Elsevier, 2018
Keywords
Morphogenesis topology, Complexity, Partially-directed evolution, Non-Archimedean analysis, Quantum models of interaction, Active information, Bohmian-like dynamics
National Category
Biological Sciences Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-76952 (URN)10.1016/j.biosystems.2018.04.004 (DOI)000436913300003 ()29758243 (PubMedID)
Available from: 2018-07-19 Created: 2018-07-19 Last updated: 2018-07-19Bibliographically approved
Khrennikov, A., Alodjants, A., Trofimova, A. & Tsarev, D. (2018). On Interpretational Questions for Quantum-Like Modeling of Social Lasing. Entropy, 20(12), Article ID 921.
Open this publication in new window or tab >>On Interpretational Questions for Quantum-Like Modeling of Social Lasing
2018 (English)In: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 20, no 12, article id 921Article in journal (Refereed) Published
Abstract [en]

The recent years were characterized by increasing interest to applications of the quantum formalism outside physics, e.g., in psychology, decision-making, socio-political studies. To distinguish such approach from quantum physics, it is called quantum-like. It is applied to modeling socio-political processes on the basis of the social laser model describing stimulated amplification of social actions. The main aim of this paper is establishing the socio-psychological interpretations of the quantum notions playing the basic role in lasing modeling. By using the Copenhagen interpretation and the operational approach to the quantum formalism, we analyze the notion of the social energy. Quantum formalizations of such notions as a social atom, s-atom, and an information field are presented. The operational approach based on the creation and annihilation operators is used. We also introduce the notion of the social color of information excitations representing characteristics linked to lasing coherence of the type of collimation. The Bose–Einstein statistics of excitations is coupled with the bandwagon effect, one of the basic effects of social psychology. By using the operational interpretation of the social energy, we present the thermodynamical derivation of this quantum statistics. The crucial role of information overload generated by the modern mass-media is emphasized. In physics laser’s resonator, the optical cavity, plays the crucial role in amplification. We model the functioning of social laser’s resonator by “distilling” the physical scheme from connection with optics. As the mathematical basis, we use the master equation for the density operator for the quantum information field.

Place, publisher, year, edition, pages
MDPI, 2018
Keywords
quantum-like models; operational approach; information interpretation of quantum theory; social laser; social energy; quantum information field; social atom; Bose–Einstein statistics; bandwagon effect; social thermodynamics; resonator of social laser; master equation for socio-information excitations
National Category
Computational Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-79080 (URN)10.3390/e20120921 (DOI)
Available from: 2018-12-05 Created: 2018-12-05 Last updated: 2018-12-10Bibliographically approved
Pourhadi, E. & Khrennikov, A. (2018). On the solutions of Cauchy problem for two classes of semi-linear pseudo-differential equations over p-adic field. P-Adic Numbers, Ultrametric Analysis, and Applications, 10(4), 322-343
Open this publication in new window or tab >>On the solutions of Cauchy problem for two classes of semi-linear pseudo-differential equations over p-adic field
2018 (English)In: P-Adic Numbers, Ultrametric Analysis, and Applications, ISSN 2070-0466, E-ISSN 2070-0474, Vol. 10, no 4, p. 322-343Article in journal (Refereed) Published
Abstract [en]

Throughout this paper, using the p-adic wavelet basis together with the help of separation of variables and the Adomian decomposition method (as a scheme in numerical analysis) we initially investigate the solution of Cauchy problem for two classes of the first and second order of pseudo-differential equations involving the pseudo-differential operators such as Taibleson fractional operator in the setting of p-adic field.

Place, publisher, year, edition, pages
Springer, 2018
Keywords
Cauchy problem; pseudo-differential equations; p-adic field; p-adic wavelet basis; Adomian decomposition method; Abel equation
National Category
Other Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-79075 (URN)10.1134/S207004661804009X (DOI)
Available from: 2018-12-05 Created: 2018-12-05 Last updated: 2018-12-10Bibliographically approved
Khrennikov, A. & Kochubei, A. N. (2018). p-Adic Analogue of the Porous Medium Equation. Journal of Fourier Analysis and Applications, 24(5), 1401-1424
Open this publication in new window or tab >>p-Adic Analogue of the Porous Medium Equation
2018 (English)In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 24, no 5, p. 1401-1424Article in journal (Refereed) Published
Abstract [en]

We consider a nonlinear evolution equation for complex-valued functions of a real positive time variable and a p-adic spatial variable. This equation is a nonArchimedean counterpart of the fractional porous medium equation. Developing, as a tool, an L1-theory of Vladimirov’s p-adic fractional differentiation operator, we prove m-accretivity of the appropriate nonlinear operator, thus obtaining the existence and uniqueness of a mild solution. We give also an example of an explicit solution of the p-adic porous medium equation.

Place, publisher, year, edition, pages
Springer, 2018
Keywords
Mild solution of the Cauchy problem; p-adic numbers; p-adic porous medium equation; Vladimirov’s p-adic fractional differentiation operator
National Category
Other Mathematics
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-72074 (URN)10.1007/s00041-017-9556-4 (DOI)000445100200010 ()
Available from: 2018-04-03 Created: 2018-04-03 Last updated: 2018-10-22Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-9857-0938

Search in DiVA

Show all publications