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.

Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.

Khrennikov, Andrei

Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.

Ohya, Masanori

Tokyo University of Science.

Tanaka, Yoshiharu

Tokyo University of Science.

Quantum-like dynamics of decision-making2012In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 391, no 5, p. 2083-2099Article in journal (Refereed)

Abstract [en]

In cognitive psychology, some experiments for games were reported, and they demonstrated that real players did not use the "rational strategy" provided by classical game theory and based on the notion of the Nasch equilibrium. This psychological phenomenon was called the disjunction effect. Recently, we proposed a model of decision making which can explain this effect ("irrationality" of players) Asano et al. (2010, 2011) [23,24]. Our model is based on the mathematical formalism of quantum mechanics, because psychological fluctuations inducing the irrationality are formally represented as quantum fluctuations Asano et al. (2011)[55]. In this paper, we reconsider the process of quantum-like decision-making more closely and redefine it as a well-defined quantum dynamics by using the concept of lifting channel, which is an important concept in quantum information theory. We also present numerical simulation for this quantum-like mental dynamics. It is non-Markovian by its nature. Stabilization to the steady state solution (determining subjective probabilities for decision making) is based on the collective effect of mental fluctuations collected in the working memory of a decision maker. (C) 2011 Elsevier B.V. All rights reserved.

Many-body cooperative energy transfer is an important process in biology, medicine, photosynthesis, rare-earth-doped laser materials, responsible for up- and down-conversion of energy, optical excitation sensitization and relaxation. We present an analytical solution for long-time asymptotic of static luminescence quenching kinetics due to cooperative energy transfer to ensembles of acceptors comprised of two-, three-, and more particles. For cooperative energy transfer and cooperative luminescence quenching to n-body acceptors we have discovered a new law of power d/(nS - (n - 1)d) time dependence (d = 1, 2, 3 is the space dimension, S = 6, 8, 10 is the multipolarty of interaction: dipole-dipole, dipole-quadrupole, or quadrupole-quadrupole). The detailed numerical simulation of cooperative quenching by Monte-Carlo method confirms the theoretical result. (C) 2012 Elsevier B.V. All rights reserved.

Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering. Matematik.

Quantum Bohmian model for financial market2007In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. Volume 374, no Issue 1, p. 304-314Article in journal (Refereed)

We consider Brownian motion in the space of fields and show that such a random field interacting with threshold type detectors produces clicks at random moments of time. The corresponding probability distribution can be approximately described by the same mathematical formalism as is used in quantum mechanics, theory of Hermitian operators in complex Hilbert space. The temporal structure of the "prequantum random field" which is the L-2-valued Wiener process plays the crucial role. Moments of detector's clicks are mathematically described as hitting times which are actively used in classical theory of stochastic processes. Born's formula appears as an approximate formula. In principle, the difference between the formula derived in this paper and the conventional Born's formula can be tested experimentally. In our model the presence of the random gain in detectors plays a crucial role. We also stress the role of the detection threshold which is not merely a technicality, but the fundamental element of the model. (C) 2013 Elsevier B.V. All rights reserved.

Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.

Genetic code on the diadic plane2007In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 381, p. 265-272Article in journal (Refereed)

In this paper we demonstrate that the probabilistic quantum-like (QL) behavior–the Born’s rule, interference of probabilities, violation of Bell’s inequality, representation of variables by in general noncommutative self-adjoint operators, Schrödinger’s dynamics–can be exhibited not only by processes in the micro world, but also in economics. In our approach the QL-behavior is induced not by properties of systems. Here systems (commodities) are macroscopic. They could not be superpositions of two different states. In our approach the QL-behavior of economical statistics is a consequence of the organization of the process of production as well as investments. In particular, Hamiltonian (“financial energy”) is determined by rate of return.