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Khrennikov, A. & Haven, E. (2023). A Brief Overview of the Quantum-Like Formalism in Social Science. In: Chakraborti, A., Haven, E., Patra, S., Singh, N. (Ed.), Quantum Decision Theory and Complexity Modelling in Economics and Public Policy: (pp. 3-9). Springer
Open this publication in new window or tab >>A Brief Overview of the Quantum-Like Formalism in Social Science
2023 (English)In: Quantum Decision Theory and Complexity Modelling in Economics and Public Policy / [ed] Chakraborti, A., Haven, E., Patra, S., Singh, N., Springer, 2023, p. 3-9Chapter in book (Refereed)
Abstract [en]

This paper provides for a general overview of some of the main areas of applications where we believe the formalism from quantum mechanics has been (and can be) fruitfully applied. Over the past decade, progress has been made on using elements of this formalism in decision making models but also in data retrieval approaches and even in areas such as finance.

Place, publisher, year, edition, pages
Springer, 2023
Series
New Economic Window, ISSN 2039-411X, E-ISSN 2039-4128
National Category
Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-126314 (URN)10.1007/978-3-031-38833-0_1 (DOI)2-s2.0-85172462437 (Scopus ID)9783031388323 (ISBN)9783031388330 (ISBN)9783031388354 (ISBN)
Available from: 2024-01-10 Created: 2024-01-10 Last updated: 2024-01-11Bibliographically approved
Ando, T., Asano, M., Khrennikov, A., Matsuoka, T. & Yamato, I. (2023). Adaptive Dynamics Simulation of Interference Phenomenon for Physical and Biological Systems. Entropy, 25(11), Article ID 1487.
Open this publication in new window or tab >>Adaptive Dynamics Simulation of Interference Phenomenon for Physical and Biological Systems
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2023 (English)In: Entropy, E-ISSN 1099-4300, Vol. 25, no 11, article id 1487Article in journal (Refereed) Published
Abstract [en]

Biological systems have been shown to have quantum-like behaviors by applying the adaptive dynamics view on their interaction networks. In particular, in the process of lactose-glucose metabolism, cells generate probabilistic interference patterns similarly to photons in the two-slit experiment. Such quantum-like interference patterns can be found in biological data, on all scales, from proteins to cognitive, ecological, and social systems. The adaptive dynamics approach covers both biological and physical phenomena, including the ones which are typically associated with quantum physics. We guess that the adaptive dynamics can be used for the clarification of quantum foundations, and the present paper is the first step in this direction. We suggest the use of an algorithm for the numerical simulation of the behavior of a billiard ball-like particle passing through two slits by explicitly considering the influence of the two-slit environment (experimental context). Our simulation successfully mimics the interference pattern obtained experimentally in quantum physics. The interference of photons or electrons by two slits is known as a typical quantum mechanical effect. We do not claim that the adaptive dynamics can reproduce the whole body of quantum mechanics, but we hope that this numerical simulation example will stimulate further extensive studies in this direction-the representation of quantum physical phenomena in an adaptive dynamical framework.

Place, publisher, year, edition, pages
MDPI, 2023
Keywords
two-slit interference, adaptive dynamics, interaction network, quantum mechanics, particle model simulation
National Category
Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-126285 (URN)10.3390/e25111487 (DOI)001118411700001 ()37998179 (PubMedID)2-s2.0-85178111056 (Scopus ID)
Available from: 2024-01-09 Created: 2024-01-09 Last updated: 2024-02-05Bibliographically approved
Khrennikov, A. (2023). Bild Conception of Scientific Theory Structuring in Classical and Quantum Physics: From Hertz and Boltzmann to Schrödinger and De Broglie. Entropy, 25(11), Article ID 1565.
Open this publication in new window or tab >>Bild Conception of Scientific Theory Structuring in Classical and Quantum Physics: From Hertz and Boltzmann to Schrödinger and De Broglie
2023 (English)In: Entropy, E-ISSN 1099-4300, Vol. 25, no 11, article id 1565Article in journal (Refereed) Published
Abstract [en]

We start with a methodological analysis of the notion of scientific theory and its interrelation with reality. This analysis is based on the works of Helmholtz, Hertz, Boltzmann, and Schrodinger (and reviews of D'Agostino). Following Helmholtz, Hertz established the "Bild conception" for scientific theories. Here, "Bild" ("picture") carries the meaning "model" (mathematical). The main aim of natural sciences is construction of the causal theoretical models (CTMs) of natural phenomena. Hertz claimed that a CTM cannot be designed solely on the basis of observational data; it typically contains hidden quantities. Experimental data can be described by an observational model (OM), often based on the price of acausality. CTM-OM interrelation can be tricky. Schrodinger used the Bild concept to create a CTM for quantum mechanics (QM), and QM was treated as OM. We follow him and suggest a special CTM for QM, so-called prequantum classical statistical field theory (PCSFT). QM can be considered as a PCSFT image, but not as straightforward as in Bell's model with hidden variables. The common interpretation of the violation of the Bell inequality is criticized from the perspective of the two-level structuring of scientific theories. Such critical analysis of von Neumann and Bell no-go theorems for hidden variables was performed already by De Broglie (and Lochak) in the 1970s. The Bild approach is applied to the two-level CTM-OM modeling of Brownian motion: the overdamped regime corresponds to OM. In classical mechanics, CTM=OM; on the one hand, this is very convenient; on the other hand, this exceptional coincidence blurred the general CTM-OM structuring of scientific theories. We briefly discuss ontic-epistemic structuring of scientific theories (Primas-Atmanspacher) and its relation to the Bild concept. Interestingly, Atmanspacher as well as Hertz claim that even classical physical theories should be presented on the basic of two-level structuring.

Place, publisher, year, edition, pages
MDPI, 2023
Keywords
Bild conception, scientific theory, Helmholtz, Hertz, Boltzmann, Schrodinger, De Broglie, quantum mechanics, Brownian motion, Bell, prequantum classical statistical field theory
National Category
Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-126025 (URN)10.3390/e25111565 (DOI)001108190200001 ()37998257 (PubMedID)2-s2.0-85178136954 (Scopus ID)
Available from: 2023-12-18 Created: 2023-12-18 Last updated: 2024-01-11Bibliographically approved
Khrennikov, A. (2023). Coherent decision making stimulated within the social laser: open quantum systems framework. Philosophical Transactions. Series A: Mathematical, physical, and engineering science, 381(2252), Article ID 20220294.
Open this publication in new window or tab >>Coherent decision making stimulated within the social laser: open quantum systems framework
2023 (English)In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 381, no 2252, article id 20220294Article, review/survey (Refereed) Published
Abstract [en]

We start with a brief review on social laser theory which is newly framed with the notion of an infon-social energy quantum carrying coarse-grained information content. Infons are the excitations of the quantum social-information field. Humans are analogues of atoms-social atoms absorbing and emitting infons. Another new development is coupling of the social laser with the decision making model based on open quantum systems. The role of the environment for social atoms is played by the strong coherent social-information field-the output of social lasing. We analyse a simple quantum master equation generating decision jumps towards the coherent decision directed by the social laser beam. As an illustrative example, we analyse the possibility to create a societal benefit laser, i.e. directed for societal benefit.This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 1)'.

Place, publisher, year, edition, pages
Royal Society, 2023
Keywords
social laser, social-information field, indistinguishability, quantum statistics, decision making, open quantum systems
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-123583 (URN)10.1098/rsta.2022.0294 (DOI)001013616000007 ()37334450 (PubMedID)2-s2.0-85162734062 (Scopus ID)
Available from: 2023-08-10 Created: 2023-08-10 Last updated: 2023-09-06Bibliographically approved
Khrennikov, A. (2023). Cooperative Functioning of Unconscious and Consciousness from Theory of Open Quantum Systems. In: Chakraborti, A., Haven, E., Patra, S., Singh, N. (Ed.), Quantum Decision Theory and Complexity Modelling in Economics and Public Policy: (pp. 11-23). Springer
Open this publication in new window or tab >>Cooperative Functioning of Unconscious and Consciousness from Theory of Open Quantum Systems
2023 (English)In: Quantum Decision Theory and Complexity Modelling in Economics and Public Policy / [ed] Chakraborti, A., Haven, E., Patra, S., Singh, N., Springer, 2023, p. 11-23Chapter in book (Refereed)
Abstract [en]

We present the mathematical model of cooperative functioning of unconscious and consciousness. The model is based on the theory of open quantum systems. Unconscious and consciousness are treated as bio-information systems. The latter plays the role a measurement apparatus for the former. States of both systems are represented in Hilbert spaces. Consciousness performs measurements on the states which are generated in unconscious. This process of unconscious-conscious interaction is described by the scheme of indirect measurements. This scheme is widely used in quantum information theory and it leads to the theory of quantum instruments (Davis-Lewis-Ozawa). Our approach is known as quantum-like modeling. It should be sharply distinguished from modeling of genuine quantum physical processes in biosystems, in particular, in the brain. In the quantum-like framework, the brain is a black box processing information in the accordance with the laws of quantum theory. During the last 10–15 years this framework has been actively used in cognition, psychology, decision making, social and political sciences. The quantum-like scheme of unconscious-consciousness functioning has already been explored for sensation-perception modeling.

Place, publisher, year, edition, pages
Springer, 2023
National Category
Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-126315 (URN)10.1007/978-3-031-38833-0_2 (DOI)2-s2.0-85172459125 (Scopus ID)9783031388323 (ISBN)9783031388330 (ISBN)
Available from: 2024-01-10 Created: 2024-01-10 Last updated: 2024-01-11Bibliographically approved
Shor, O., Yaniv-Rosenfeld, A., Valevski, A., Weizman, A., Khrennikov, A. & Benninger, F. (2023). EEG-based spatio-temporal relation signatures for the diagnosis of depression and schizophrenia. Scientific Reports, 13(1), Article ID 776.
Open this publication in new window or tab >>EEG-based spatio-temporal relation signatures for the diagnosis of depression and schizophrenia
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2023 (English)In: Scientific Reports, E-ISSN 2045-2322, Vol. 13, no 1, article id 776Article in journal (Refereed) Published
Abstract [en]

The diagnosis of psychiatric disorders is currently based on a clinical and psychiatric examination (intake). Ancillary tests are used minimally or only to exclude other disorders. Here, we demonstrate a novel mathematical approach based on the field of p-adic numbers and using electroencephalograms (EEGs) to identify and differentiate patients with schizophrenia and depression from healthy controls. This novel approach examines spatio-temporal relations of single EEG electrode signals and characterizes the topological structure of these relations in the individual patient. Our results indicate that the relational topological structures, characterized by either the personal universal dendrographic hologram (DH) signature (PUDHS) or personal block DH signature (PBDHS), form a unique range for each group of patients, with impressive correspondence to the clinical condition. This newly developed approach results in an individual patient signature calculated from the spatio-temporal relations of EEG electrodes signals and might help the clinician with a new objective tool for the diagnosis of a multitude of psychiatric disorders.

Place, publisher, year, edition, pages
Nature Publishing Group, 2023
National Category
Psychiatry Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-119964 (URN)10.1038/s41598-023-28009-0 (DOI)000935602800007 ()36641536 (PubMedID)2-s2.0-85146271587 (Scopus ID)
Note

Correction published in: Author Correction: EEG-based spatio-temporal relation signatures for the diagnosis of depression and schizophrenia (Mar, 10.1038/s41598-023-28009-0, 2023). Scientific Reports. Vol 13, Iss 1, Articleno 4644, DOI10.1038/s41598-023-31604-w

Available from: 2023-03-27 Created: 2023-03-27 Last updated: 2023-09-15Bibliographically approved
Khrennikov, A. & Basieva, I. (2023). Entanglement of Observables: Quantum Conditional Probability Approach. Foundations of physics, 53, Article ID 84.
Open this publication in new window or tab >>Entanglement of Observables: Quantum Conditional Probability Approach
2023 (English)In: Foundations of physics, ISSN 0015-9018, E-ISSN 1572-9516, Vol. 53, article id 84Article in journal (Refereed) Published
Abstract [en]

This paper is devoted to clarification of the notion of entanglement through decoupling it from the tensor product structure and treating as a constraint posed by probabilistic dependence of quantum observable A and B. In our framework, it is meaningless to speak about entanglement without pointing to the fixed observables A and B,  so this is AB-entanglement. Dependence of quantum observables is formalized as non-coincidence of conditional probabilities. Starting with this probabilistic definition, we achieve the Hilbert space characterization of the AB-entangled states as amplitude non-factorisable states. In the tensor product case, AB-entanglement implies standard entanglement, but not vise verse. AB-entanglement for dichotomous observables is equivalent to their correlation, i.e., ⟨AB⟩�≠⟨A⟩�⟨B⟩�. We describe the class of quantum states that are AuBu-entangled for a family of unitary operators (u). Finally, observables entanglement is compared with dependence of random variables in classical probability theory.

Place, publisher, year, edition, pages
Springer, 2023
National Category
Mathematics Physical Sciences
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-126323 (URN)10.1007/s10701-023-00725-7 (DOI)2-s2.0-85171588972 (Scopus ID)
Available from: 2024-01-10 Created: 2024-01-10 Last updated: 2024-01-11Bibliographically approved
Ozawa, M. & Khrennikov, A. (2023). Nondistributivity of human logic and violation of response replicability effect in cognitive psychology. Journal of mathematical psychology (Print), 112, Article ID 102739.
Open this publication in new window or tab >>Nondistributivity of human logic and violation of response replicability effect in cognitive psychology
2023 (English)In: Journal of mathematical psychology (Print), ISSN 0022-2496, E-ISSN 1096-0880, Vol. 112, article id 102739Article in journal (Refereed) Published
Abstract [en]

The aim of this paper is to promote quantum logic as one of the basic tools for analyzing human reasoning. We compare it with classical (Boolean) logic and highlight the role of violation of the distributive law for conjunction and disjunction. It is well known that nondistributivity is equivalent to incompatibility of logical variables — the impossibility to assign jointly the two-valued truth values to these variables. A natural question arises as to whether quantum logical nondistributivity in human logic can be tested experimentally. We show that testing the response replicability effect (RRE) in cognitive psychology is equivalent to testing nondistributivity — under the prevailing conjecture that the mental state update generated by observation is described as orthogonal projection of the mental state vector (the projective update conjecture of Wang and Busemeyer). A simple test of RRE is suggested. In contrast to the previous works in quantum-like modeling, we proceed in the state-dependent framework; in particular, distributivity, compatibility, and RRE are considered in a fixed mental state. In this framework, we improve the previous result on the impossibility to combine question order and response replicability effects by using (von Neumann–Lüders) projective measurements.

Place, publisher, year, edition, pages
Elsevier, 2023
National Category
Mathematics Psychology
Research subject
Mathematics, Applied Mathematics; Social Sciences, Psychology
Identifiers
urn:nbn:se:lnu:diva-120377 (URN)10.1016/j.jmp.2022.102739 (DOI)000950868800001 ()2-s2.0-85144761197 (Scopus ID)
Available from: 2023-04-20 Created: 2023-04-20 Last updated: 2023-05-29Bibliographically approved
Dragovich, B., Khrennikov, A., Kozyrev, S. V. & Volovich, I. V. (2023). On the Occasion of the Centenary of the Birth of V. S. Vladimirov (1923-2012). P-Adic Numbers, Ultrametric Analysis, and Applications, 15(3), 243-244
Open this publication in new window or tab >>On the Occasion of the Centenary of the Birth of V. S. Vladimirov (1923-2012)
2023 (English)In: P-Adic Numbers, Ultrametric Analysis, and Applications, ISSN 2070-0466, E-ISSN 2070-0474, Vol. 15, no 3, p. 243-244Article in journal, Editorial material (Other academic) Published
Abstract [en]

In this note, on the occasion of the centenary of the birth, we are remembering Vasilii Sergeevich Vladimirov as an outstanding scientist and his contributions to pure and applied mathematics, especiallyp-adic analysis and its applications.

Place, publisher, year, edition, pages
Springer, 2023
Keywords
V. S. Vladimirov, p-adic analysis and its applications
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-125915 (URN)10.1134/S2070046623030056 (DOI)001098970900005 ()2-s2.0-85175876096 (Scopus ID)
Available from: 2023-12-08 Created: 2023-12-08 Last updated: 2024-01-11Bibliographically approved
Khrennikov, A. (2023). Open Quantum Systems in Biology, Cognitive and Social Sciences. Springer
Open this publication in new window or tab >>Open Quantum Systems in Biology, Cognitive and Social Sciences
2023 (English)Book (Refereed)
Abstract [en]

This book mathematically analyzes the basic problems of biology, decision making and psychology within the framework of the theory of open quantum systems.

 

In recent years there has been an explosion of interest in applications of quantum theory in fields beyond physics. The main areas include psychology, decision-making, economics, finance, social science as well as genetics and molecular biology. The corresponding models are referred to as quantum-like; they don’t concern any genuine physical processes in the human brain.

Quantum-like models reflect the special features of information processing in biological, cognitive, and social systems which match well with the quantum formalism. This formalism gives rise to the quantum probability model (QP) which differs essentially from Kolmogorov's classical probability model. QP also serves as the basis for quantum information theory.

Recently QP has been widely applied to the resolution of the basic paradoxes of decision making theory and to modeling experimental data stemming from cognition, psychology, economics, and finance thereby shedding light on probability fallacies and irrational behavior.

In this book, the theory of quantum instruments and the quantum master equation are applied to the modeling of biological and cognitive processes, in particular, to the stability of complex biological and social systems interacting with their environment. An essential part of the book is devoted to the theory of the social laser and the Fröhlich condensate. 

Place, publisher, year, edition, pages
Springer, 2023. p. 371
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-126299 (URN)10.1007/978-3-031-29024-4 (DOI)2-s2.0-85159400723 (Scopus ID)9783031290237 (ISBN)9783031290268 (ISBN)9783031290244 (ISBN)
Available from: 2024-01-09 Created: 2024-01-09 Last updated: 2024-01-11Bibliographically approved
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-9857-0938

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