195 research outputs found
On possible violation of the CHSH Bell inequality in a classical context
It has been shown that there is a small possibility to experimentally violate
the CHSH Bell inequality in a 'classical' context. The probability of such a
violation has been estimated in the framework of a classical probabilistic
model in the language of a random-walk representation.Comment: 9 pages, 1 figur
Generalized probabilities taking values in non-Archimedean fields and topological groups
We develop an analogue of probability theory for probabilities taking values
in topological groups. We generalize Kolmogorov's method of axiomatization of
probability theory: main distinguishing features of frequency probabilities are
taken as axioms in the measure-theoretic approach. We also present a review of
non-Kolmogorovian probabilistic models including models with negative, complex,
and -adic valued probabilities. The latter model is discussed in details.
The introduction of -adic (as well as more general non-Archimedean)
probabilities is one of the main motivations for consideration of generalized
probabilities taking values in topological groups which are distinct from the
field of real numbers. We discuss applications of non-Kolmogorovian models in
physics and cognitive sciences. An important part of this paper is devoted to
statistical interpretation of probabilities taking values in topological groups
(and in particular in non-Archimedean fields)
On consistency of the quantum-like representation algorithm
In this paper we continue to study so called ``inverse Born's rule problem'':
to construct representation of probabilistic data of any origin by a complex
probability amplitude which matches Born's rule. The corresponding algorithm --
quantum-like representation algorithm (QLRA) was recently proposed by A.
Khrennikov [1]--[5]. Formally QLRA depends on the order of conditioning. For
two observables and - and conditional probabilities
produce two representations, say in Hilbert spaces and
In this paper we prove that under natural assumptions these two representations
are unitary equivalent. This result proves consistency QLRA
Distributivity breaking and macroscopic quantum games
Examples of games between two partners with mixed strategies, calculated by
the use of the probability amplitude as some vector in Hilbert space are given.
The games are macroscopic, no microscopic quantum agent is supposed. The reason
for the use of the quantum formalism is in breaking of the distributivity
property for the lattice of yes-no questions arising due to the special rules
of games. The rules of the games suppose two parts: the preparation and
measurement. In the first part due to use of the quantum logical
orthocomplemented non-distributive lattice the partners freely choose the wave
functions as descriptions of their strategies. The second part consists of
classical games described by Boolean sublattices of the initial non-Boolean
lattice with same strategies which were chosen in the first part. Examples of
games for spin one half are given. New Nash equilibria are found for some
cases. Heisenberg uncertainty relations without the Planck constant are written
for the "spin one half game"
Contextuality-by-Default: A Brief Overview of Ideas, Concepts, and Terminology
This paper is a brief overview of the concepts involved in measuring the
degree of contextuality and detecting contextuality in systems of binary
measurements of a finite number of objects. We discuss and clarify the main
concepts and terminology of the theory called "contextuality-by-default," and
then discuss a possible generalization of the theory from binary to arbitrary
measurements.Comment: Lecture Notes in Computer Science 9535 (with the corrected list of
authors) (2016
Phase transitions for -adic Potts model on the Cayley tree of order three
In the present paper, we study a phase transition problem for the -state
-adic Potts model over the Cayley tree of order three. We consider a more
general notion of -adic Gibbs measure which depends on parameter
\rho\in\bq_p. Such a measure is called {\it generalized -adic quasi Gibbs
measure}. When equals to -adic exponent, then it coincides with the
-adic Gibbs measure. When , then it coincides with -adic quasi
Gibbs measure. Therefore, we investigate two regimes with respect to the value
of . Namely, in the first regime, one takes for some
J\in\bq_p, in the second one . In each regime, we first find
conditions for the existence of generalized -adic quasi Gibbs measures.
Furthermore, in the first regime, we establish the existence of the phase
transition under some conditions. In the second regime, when we prove the existence of a quasi phase transition. It turns out that
if and \sqrt{-3}\in\bq_p, then one finds the existence
of the strong phase transition.Comment: 27 page
p-Adic Mathematical Physics
A brief review of some selected topics in p-adic mathematical physics is
presented.Comment: 36 page
Dynamics of laser-driven proton acceleration exhibited by measured laser absorptivity and reflectivity
Proton acceleration from nanometer thin foils with intense laser pulses is investigated experimentally. We analyzed the laser absorptivity by parallel monitoring of laser transmissivity and reflectivity with different laser intensities when moving the targets along the laser axis. A direct correlation between laser absorptivity and maximum proton energy is observed. Experimental results are interpreted in analytical estimation, exhibiting a coexistence of plasma expansion and light-sail form of radiation pressure acceleration (RPA-LS) mechanisms during the entire proton acceleration process based on the measured laser absorptivity and reflectivity
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