| 1. |
- Accardi, Luigi, et al.
(author)
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Quantum Markov Model for Data from Shafir-Tversky Experiments in Cognitive Psychology
- 2009
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In: Open systems & information dynamics. - Singapore : WSP. - 1230-1612 .- 1573-1324. ; 16:4, s. 371-385
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Journal article (peer-reviewed)abstract
- We analyze, from the point of view of quantum probability, statistical data from two interesting experiments, done by Shafir and Tversky [1, 2] in the domain of cognitive psychology. These are gambling experiments of Prisoner Dilemma type. They have important consequences for economics, especially for the justification of the Savage "Sure Thing Principle" [3] (implying that agents of the market behave rationally). Data from these experiments were astonishing, both from the viewpoint of cognitive psychology and economics and probability theory. Players behaved irrationally. Moreover, all attempts to generate these data by using classical Markov model were unsuccessful. In this note we show (by inventing a simple statistical test — generalized detailed balance condition) that these data are non-Kolmogorovian. We also show that it is neither quantum (i.e., it cannot be described by Dirac-von Neumann model). We proceed towards a quantum Markov model for these data.
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| 3. |
- Albeverio, S., et al.
(author)
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Operator calculus for p-adic valued symbols and quantization
- 2009
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In: Rendicoti Del Seminario Matematico. - 0373-1243. ; 67:2, s. 137-150
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Journal article (peer-reviewed)abstract
- The aim of this short review is to attract the attention of the pseudo-differentialcommunity to possibilities in the development of operator calculus for symbols (dependingon p-adic conjugate variables) taking values in fields of p-adic numbers. Essentials of thiscalculus were presented in works of the authors of this paper in order to perform p-adic valuedquantization. Unfortunately, this calculus still has not attracted a great deal of attentionfrom pure mathematicians, although it opens new and interesting domains for the theory ofpseudo-differential operators.
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| 4. |
- Albeverio, Sergio, et al.
(author)
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p-Adic valued quantization
- 2009
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In: P-Adic Numbers, Ultrametric Analysis, and Applications. - Berlin : Springer. - 2070-0466 .- 2070-0474. ; 1:2, s. 91-104
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Research review (peer-reviewed)abstract
- This review covers an important domain of p-adic mathematical physics — quantum mechanics with p-adic valued wave functions. We start with basic mathematical constructions of this quantum model: Hilbert spaces over quadratic extensions of the field of p-adic numbers ℚ p , operators — symmetric, unitary, isometric, one-parameter groups of unitary isometric operators, the p-adic version of Schrödinger’s quantization, representation of canonical commutation relations in Heisenberg andWeyl forms, spectral properties of the operator of p-adic coordinate.We also present postulates of p-adic valued quantization. Here observables as well as probabilities take values in ℚ p . A physical interpretation of p-adic quantities is provided through approximation by rational numbers.
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| 6. |
- Avis, David, et al.
(author)
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Single, Complete, Probability Spaces Consistent With EPR-Bohm-Bell Experimental Data
- 2009
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In: Foundations of Probability and Physics-5. - USA : American Institute of Physics (AIP). - 9780735406360 ; , s. 294-301
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Conference paper (peer-reviewed)abstract
- Weshow that paradoxical consequences of violations of Bell's inequality areinduced by the use of an unsuitable probabilistic description forthe EPR-Bohm-Bell experiment. The conventional description (due to Bell) isbased on a combination of statistical data collected for differentsettings of polarization beam splitters (PBSs). In fact, such dataconsists of some conditional probabilities which only partially define aprobability space. Ignoring this conditioning leads to apparent contradictions inthe classical probabilistic model (due to Kolmogorov). We show howto make a completely consistent probabilistic model by taking intoaccount the probabilities of selecting the settings of the PBSs.Our model matches both the experimental data and is consistentwith classical probability theory.
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| 10. |
- Dragovich, B., et al.
(author)
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On p-adic mathematical physics
- 2009
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In: P-Adic Numbers, Ultrametric Analysis, and Applications. - Berlin : Springer. - 2070-0466 .- 2070-0474. ; 1:1, s. 1-17
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Research review (peer-reviewed)abstract
- A brief review of some selected topics in p-adic mathematical physics is presented.
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