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Andrei Khrennikov published an article in April 2018.
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202 shared publications
121 shared publications
111 shared publications
Max Planck Institute of Quantum Optics (MPQ), Hans-Kopfermann-Str. 1, 85748 Garching, Germany
I. V. Volovich
105 shared publications
92 shared publications
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(2003 - 2018)
(2003 - 2018)
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Article 0 Reads 0 Citations A stochastic p-adic model of the capillary flow in porous random medium Published: 01 April 2018
Physica A: Statistical Mechanics and its Applications, doi: 10.1016/j.physa.2018.03.049
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 ultrametric 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.
Article 0 Reads 1 Citation From axiomatics of quantum probability to modelling geological uncertainty and management of intelligent hydrocarbon res... Published: 19 March 2018
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, doi: 10.1098/rsta.2017.0225
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 from 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).
Article 0 Reads 0 Citations Social laser model: from color revolutions to Brexit and election of Donald Trump Published: 05 February 2018
Kybernetes, doi: 10.1108/k-03-2017-0101
This paper aims to present the basic assumptions for creation of social lasers and attract attention of other researchers (both from physics and socio-political science) to the problem of modeling of Stimulated Amplification of Social Actions (SASA). The model of SASA and its analysis are based on the mathematical formalism of quantum thermodynamics and field theory (applied outside of physics). The presented quantum-like model provides the consistent operational model of such complex socio-political phenomenon as SASA. The model of SASA is heavily based on the use of the notion of social energy. This notion has not yet been formalized. Evidence of SASA (“functioning of social lasers”) is rapidly accumulating, from color revolutions to such democratically structured protest actions as Brexit and the recent election of Donald Trump as the President of the USA. The corresponding socio-political studies are characterized by diversity of opinions and conclusions. The presented social laser model can be used to clarify these complex socio-political events and even predict their possibility. SASA is the powerful source of social instability. Understanding its informational structure and origin may help to stabilize the modern society. Application of the quantum-like model of laser technology in social and political sciences is really a novel and promising approach.
Article 0 Reads 0 Citations Quantum-like model of subjective expected utility Published: 01 February 2018
Journal of Mathematical Economics, doi: 10.1016/j.jmateco.2018.02.001
We present a very general quantum-like model of lottery selection based on representation of beliefs of an agent by pure quantum states. Subjective probabilities are mathematically realized in the framework of quantum probability (QP). Utility functions are borrowed from the classical decision theory. But in the model they are represented not only by their values. Heuristically one can say that each value ui=u(xi)ui=u(xi) is surrounded by a cloud of information related to the event (A,xi).(A,xi). An agent processes this information by using the rules of quantum information and QP. This process is very complex; it combines counterfactual reasoning for comparison between preferences for different outcomes of lotteries which are in general compelementary. These comparisons induce interference type effects (constructive or destructive). The decision process is mathematically represented by the comparison operator and the outcome of this process is determined by the sign of the value of corresponding quadratic form on the belief state. This operational process can be decomposed into a few subprocesses. Each of them can be formally treated as a comparison of subjective expected utilities and interference factors (the latter express, in particular, risks related to lottery selection). The main aim of this paper is to analyze the mathematical structure of these processes in the most general situation: representation of lotteries by noncommuting operators.
Article 0 Reads 0 Citations Bohr against Bell: complementarity versus nonlocality Published: 22 November 2017
Open Physics, doi: 10.1515/phys-2017-0086
In this note we compare the views of Bohr (known as the Copenhagen interpretation of quantum mechanics) with the views of Bell: complementarity versus nonlocality.
Article 0 Reads 1 Citation Quantum Bayesian perspective for intelligence reservoir characterization, monitoring and management Published: 02 October 2017
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, doi: 10.1098/rsta.2016.0398
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 Växjö 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’.