arXiv subjects

V. I. Yukalov

Publications and source records attributed to V. I. Yukalov.

At least 55 records · Page 3Linked to original sources

arXiv2022

Quantum Uncertainty in Decision Theory

An approach is presented treating decision theory as a probabilistic theory based on quantum techniques. Accurate definitions are given and thorough analysis is accomplished for the quantum probabilities describing the choice between separate alternatives, sequential alternatives characterizing conditional quantum probabilities, and behavioral quantum probabilities taking into account rational-irrational duality of decision making. The comparison between quantum and classical probabilities is explained. The analysis demonstrates that quantum probabilities serve as an essentially more powerful tool of characterizing various decision-making situations including the influence of psychological behavioral effects.

cs.AI↗

arXiv2022

Self-excited waves in complex social systems

A social system is considered whose agents choose between several alternatives of possible actions. The system is described by the fractions of agents preferring the corresponding alternatives. The agents interact with each other by exchanging information on their choices. Each alternative is characterized by three attributes: utility, attractiveness, and replication. The agents are heterogeneous having different initial conditions and different types of memory, which can be long-term or short-term. The agent interactions, generally, can depend on the distance between the agents, varying from short-range to long-range interactions. The emphasis in the paper is on long-range interactions. In a mixed society consisting of agents with both long-term and short-term memory, there appears the effect of spontaneous excitation of preference waves, when the fractions of agents preferring this or that alternative suddenly start strongly oscillating, either periodically or chaotically. Since the considered society forms a closed system, without any external influence, the arising waves are internally self-excited by the society.

physics.soc-ph↗

arXiv2022

Calculating critical temperature and critical exponents by self-similar approximants

Self-similar approximation theory allows for defining effective sums of asymptotic series. The method of self-similar factor approximants is applied for calculating the critical temperature and critical exponents of the $O(N)$-symmetric $φ^4$ field theory in three dimensions by summing asymptotic $\varepsilon$ expansions. This method is shown to be essentially simpler than other summation techniques involving complicated numerical calculations, while enjoying comparable accuracy.

cond-mat.stat-mech↗

arXiv2022

Role of collective information in networks of quantum operating agents

A network of agents is considered whose decision processes are described by the quantum decision theory previously advanced by the authors. Decision making is done by evaluating the utility of alternatives, their attractiveness, and the available information, whose combinations form the probabilities to choose a given alternative. As a result of the interplay between these three contributions, the process of choice between several alternatives is multimodal. The agents interact by exchanging information, which can take two forms: (i) information that an agent can directly receive from another agent and (ii) information collectively created by the members of the society. The information field common to all agents tends to smooth out sharp variations in the temporal behaviour of the probabilities and can even remove them. For agents with short-term memory, the probabilities often tend to their limiting values through strong oscillations and, for a range of parameters, these oscillations last for ever, representing an ever lasting hesitation of the decision makers. Switching on the information field makes the amplitude of the oscillations smaller and even can halt the everlasting oscillations forcing the probabilities to converge to fixed limits. The dynamic disjunction effect is described.

physics.soc-ph↗

arXiv2022

Triggering spin reversal in nanomolecules and nanoclusters on demand

Spin reversal in magnetic nanomolecules and nanoclusters is considered. A method is suggested allowing, from one side, to keep for long time magnetic polarization in a metastable state and, from the other side, for starting the reversal process at any required time. This method can find applications for the operation of storage memory devices and for the regulation of processes in spintronics.

cond-mat.mes-hall↗

arXiv2022

Quantification of emotions in decision making

The problem of quantification of emotions in the choice between alternatives is considered. The alternatives are evaluated in a dual manner. From one side, they are characterized by rational features defining the utility of each alternative. From the other side, the choice is affected by emotions labeling the alternatives as attractive or repulsive, pleasant or unpleasant. A decision maker needs to make a choice taking into account both these features, the utility of alternatives and their attractiveness. The notion of utility is based on rational grounds, while the notion of attractiveness is vague and rather is based on irrational feelings. A general method, allowing for the quantification of the choice combining rational and emotional features is described. Despite that emotions seem to avoid precise quantification, their quantitative evaluation is possible at the aggregate level. The analysis of a series of empirical data demonstrates the efficiency of the approach, including the realistic behavioral problems that cannot be treated by the standard expected utility theory.

cs.AI↗

arXiv2022

Methods of Retrieving Large-Variable Exponents

Methods of determining, from small-variable asymptotic expansions, the characteristic exponents for variables tending to infinity are analyzed. The following methods are considered: diff-log Padé summation, self-similar factor approximation, self-similar diff-log summation, self-similar Borel summation, and self-similar Borel-Leroy summation. Several typical problems are treated. The comparison of the results shows that all these methods provide close estimates for the large-variable exponents. The reliable estimates are obtained when different methods of summation are compatible with each other.

cond-mat.stat-mech↗

arXiv2022

Self-similar sequence transformation for critical exponents

Self-similar sequence transformation is an original type of nonlinear sequence transformations allowing for defining effective limits of asymptotic sequences. The method of self-similar factor transformations is shown to be regular. This method is applied for calculating the critical exponents of the $O(N)$-symmetric $φ^4$ theory in three dimensions by summing asymptotic $\varepsilon$ expansions. It is shown that this method is straightforward and essentially simpler than other summation techniques involving complicated numerical calculations, while enjoying comparable accuracy.

cond-mat.stat-mech↗

arXiv2022

Statistical theory of structures with extended defects

Many materials contain extended defects of nanosize scale, such as dislocations, cracks, pores, polymorphic inclusions, and other embryos of competing phases. When one is interested not in the precise internal structure of a sample with such defects, but in its overall properties as a whole, one needs a statistical picture giving a spatially averaged description. In this chapter, an approach is presented for a statistical description of materials with extended nanosize defects. A method is developed allowing for the reduction of the problem to the consideration of a set of system replicas representing homogeneous materials characterized by effective renormalized Hamiltonians. This is achieved by defining a procedure of averaging over heterophase configurations. The method is illustrated by a lattice model with randomly distributed regions of disorder.

cond-mat.stat-mech↗

arXiv2021

Zeroth-Order Nucleation Transition under Nanoscale Phase Separation

Materials with nanoscale phase separation are considered. A system representing a heterophase mixture of ferromagnetic and paramagnetic phases is studied. After averaging over phase configurations, a renormalized Hamiltonian is derived describing the coexisting phases. The system is characterized by direct and exchange interactions and an external magnetic field. The properties of the system are studied numerically. The stability conditions define the stable state of the system. At a temperature of zero, the system is in a pure ferromagnetic state. However, at finite temperature, for some interaction parameters, the system can exhibit a zeroth-order nucleation transition between the pure ferromagnetic phase and the mixed state with coexisting ferromagnetic and paramagnetic phases. At the nucleation transition, the finite concentration of the paramagnetic phase appears via a jump.

cond-mat.mes-hall↗

arXiv2021

A Resolution of St. Petersburg Paradox

The St. Petersburg paradox is the oldest paradox in decision theory and has played a pivotal role in the introduction of increasing concave utility functions embodying risk aversion and decreasing marginal utility of gains. All attempts to resolve it have considered some variants of the original set-up, but the original paradox has remained unresolved, while the proposed variants have introduced new complications and problems. Here a rigorous mathematical resolution of the St. Petersburg paradox is suggested based on a probabilistic approach to decision theory.

math.OC↗

arXiv2021

From Asymptotic Series to Self-Similar Approximants

The review presents the development of an approach of constructing approximate solutions to complicated physics problems, starting from asymptotic series, through optimized perturbation theory, to self-similar approximation theory. The close interrelation of underlying ideas of these theories is emphasized. Applications of the developed approach are illustrated by typical examples demonstrating that it combines simplicity with good accuracy.

cond-mat.stat-mech↗

arXiv2021

Self-similar extrapolation of nonlinear problems from small-variable to large-variable limit

Complicated physical problems usually are solved by resorting to perturbation theory leading to solutions in the form of asymptotic series in powers of small parameters. However, finite, and even large values of the parameters often are of the main physical interest. A method is described for predicting the large-variable behavior of solutions to nonlinear problems from the knowledge of only their small-variable expansions. The method is based on self-similar approximation theory resulting in self-similar factor approximants. The latter can well approximate a large class of functions, rational, irrational, and transcendental. The method is illustrated by several examples from statistical and condensed matter physics, where the self-similar predictions can be compared with the available large-variable behavior. It is shown that the method allows for finding the behavior of solutions at large variables when knowing just a few terms of small-variable expansions. Numerical convergence of approximants is demonstrated.

math-ph↗

arXiv2021

Hartree-Fock-Bogolubov method in the theory of Bose-condensed systems

The Hohenberg-Martin dilemma of conserving versus gapless theories for systems with Bose-Einstein condensate is considered. This dilemma states that, generally, a theory characterizing a system with broken global gauge symmetry, which is necessary for Bose-Einstein condensation, is either conserving, but has a gap in its spectrum, or is gapless, but does not obey conservation laws. In other words, such a system either displays a gapless spectrum, which is necessary for condensate existence, but is not conserving, which implies that it corresponds to an unstable system, or it respects conservation laws, describing a stable system, but the spectrum acquires a gap, which means that the condensate cannot appear. An approach is described, resolving this dilemma, and it is shown to give good quantitative agreement with experimental data. Calculations are accomplished in the Hartree-Fock-Bogolubov approximation.

cond-mat.quant-gas↗

arXiv2021

Interplay Between Approximation Theory and Renormalization Group

The review presents general methods for treating complicated problems that cannot be solved exactly and whose solution encounters two major difficulties. First, there are no small parameters allowing for the safe use of perturbation theory in powers of these parameters, and even when small parameters exist, the related perturbative series are strongly divergent. Second, such perturbative series in powers of these parameters are rather short, so that the standard resummation techniques either yield bad approximations or are not applicable at all. The emphasis in the review is on the methods advanced and developed by the author. One of the general methods is {\it Optimized Perturbation Theory} now widely employed in various branches of physics, chemistry, and applied mathematics. The other powerful method is {\it Self-Similar Approximation Theory} allowing for quite simple and accurate summation of divergent series. These theories share many common features with the method of renormalization group, which is briefly sketched in order to stress the similarities in their ideas and their mutual interconnection.

hep-th↗

arXiv2021

Self-similar extrapolation in quantum field theory

Calculations in field theory are usually accomplished by employing some variants of perturbation theory, for instance using loop expansions. These calculations result in asymptotic series in powers of small coupling parameters, which as a rule are divergent for finite values of the parameters. In this paper, a method is described allowing for the extrapolation of such asymptotic series to finite values of the coupling parameters, and even to their infinite limits. The method is based on self-similar approximation theory. This theory approximates well a large class of functions, rational, irrational, and transcendental. A method is presented, resulting in self-similar factor approximants allowing for the extrapolation of functions to arbitrary values of coupling parameters from only the knowledge of expansions in powers of small coupling parameters. The efficiency of the method is illustrated by several problems of quantum field theory.

hep-ph↗

arXiv2021

Tossing Quantum Coins and Dice

The procedure of tossing quantum coins and dice is described. This case is an important example of a quantum procedure because it presents a typical framework employed in quantum information processing and quantum computing. The emphasis is on the clarification of the difference between quantum and classical conditional probabilities. These probabilities are designed for characterizing different systems, either quantum or classical, and they, generally, cannot be reduced to each other. Thus the Lüders probability cannot be treated as a generalization of the classical conditional probability. The analogies between quantum theory of measurements and quantum decision theory are elucidated.

quant-ph↗

arXiv2020

From optical lattices to quantum crystals

Optical lattices can be loaded with atoms which can have strong interactions, such that the interaction of atoms at different lattice sites cannot be neglected. Moreover, the intersite interactions can be so strong that it can force the atoms to form a self-organized lattice, such that exists in crystals. With increasing intersite interactions, there can appear several lattice states, including conducting optical lattices, insulating optical lattices, delocalized quantum crystals, and localized quantum crystals.

cond-mat.quant-gas↗